Details

analyze106.0ms (0.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	50%	0.1%	0%	50%	0%	2
0%	0%	50%	0.1%	0%	50%	0%	3
0%	0%	50%	0.1%	0%	50%	0%	4
25%	12.5%	37.5%	0.1%	0%	50%	0%	5
26.7%	12.5%	34.3%	0.1%	0%	53.1%	0%	6
37%	15.6%	26.5%	0.1%	1.6%	54.6%	1.6%	7
40.8%	15.6%	22.6%	0.1%	2.3%	57%	2.3%	8
49.4%	17.2%	17.6%	0.1%	3.5%	58.1%	3.5%	9
53.3%	17.2%	15%	0.1%	4.1%	59.5%	4.1%	10
59.5%	18%	12.2%	0.1%	4.8%	60.2%	4.8%	11
62.5%	18%	10.8%	0.1%	5.1%	60.9%	5.1%	12

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample2.6s (3%)

Results

1.3s	8256×	body	256	valid
702.0ms	1343×	body	1024	invalid
222.0ms	724×	body	512	invalid
189.0ms	1611×	body	256	invalid
106.0ms	462×	body	256	infinite
60.0ms	259×	body	256	unsamplable

Bogosity

preprocess58.0ms (0.1%)

Algorithm

2×	egg-herbie

Rules

454×	`neg-mul-1_binary64`
436×	`fma-def_binary64`
428×	`unswap-sqr_binary64`
424×	`div-sub_binary64`
419×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	50
1	52	44
2	119	44
3	257	44
4	670	44
5	1879	40
6	4230	40
7	7364	40
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2)))

Outputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2)))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 2 (*.f64 (PI.f64) k)) (-.f64 1/2 (/.f64 n 2))))
(/.f64 (pow.f64 (.f64 k (.f64 2 (PI.f64))) (/.f64 (-.f64 1 n) 2)) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 k (.f64 2 (PI.f64))) (+.f64 1/2 (/.f64 n -2))) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 k (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 n))) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 k 2)) (fma.f64 -1/2 n 1/2)) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 k (.f64 2 (PI.f64))) (fma.f64 n -1/2 1/2)) (sqrt.f64 n))

Compiler

Compiled 20 to 17 computations (15% saved)

simplify39.0ms (0%)

Algorithm

1×	egg-herbie

Rules

667×	`associate-/l*_binary64`
561×	`associate-/r*_binary64`
453×	`div-sub_binary64`
450×	`distribute-frac-neg_binary64`
416×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	68	22
3	141	22
4	360	22
5	983	20
6	2213	20
7	5663	20

Stop Event

1×	node limit

Counts

1 → 7

Calls

Call 1

Inputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Outputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

eval2.0ms (0%)

Compiler: Compiled 102 to 64 computations (37.3% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	5	2	7
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	5	3	8

Error

0.4b

Counts

8 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.4b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
▶	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize25.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	0.3b	(/.f64 1 (sqrt.f64 k))
✓	0.3b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))

Compiler

Compiled 56 to 38 computations (32.1% saved)

series5.4s (6.3%)

Counts

4 → 40

Calls

18 calls:

Time	Variable		Point	Expression
1.2s	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
927.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
918.0ms	k	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
784.0ms	k	@	-inf	(/.f64 1 (sqrt.f64 k))
565.0ms	k	@	inf	(/.f64 1 (sqrt.f64 k))

Compiler

Compiled 501724 to 387946 computations (22.7% saved)

rewrite67.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

751×	`log-prod_binary64`
382×	`pow2_binary64`
265×	`pow1/3_binary64`
260×	`expm1-udef_binary64`
259×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	53
1	307	51
2	3926	47

Stop Event

1×	node limit

Counts

4 → 105

Calls

Call 1

Inputs
(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
(/.f64 1 (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (.f64 2 (PI.f64)) n)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 n (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 (-.f64 1/2 (.f64 k 1/2))) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 k -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.f64 k) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 k) -1) (cbrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 k -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 k) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 k -1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 -1/2 (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 k)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (*.f64 -1/2 (log.f64 k)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 (sqrt.f64 k) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (.f64 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4)) (pow.f64 k 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 1) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) -1) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)))) 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k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 2 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 2 (.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 2 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 1))))))

simplify85.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

748×	`fma-def_binary64`
360×	`log-prod_binary64`
279×	`times-frac_binary64`
207×	`sqr-pow_binary64`
205×	`exp-prod_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	289	2765
1	659	2578
2	2357	2214
3	6342	2208

Stop Event

1×	node limit

Counts

145 → 173

Calls

Call 1

Inputs
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2)
(+.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (+.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (+.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (+.f64 (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 1/6 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64))))) 3) (pow.f64 k 3)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))) (sqrt.f64 k))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(+.f64 0 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
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(.f64 1 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 1)
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(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (.f64 k 1/2))))
(.f64 (pow.f64 n (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))))
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(.f64 (pow.f64 2 (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (.f64 k 1/2))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (*.f64 k 1/2))))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (*.f64 k 1/2))))
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(-.f64 (exp.f64 (log1p.f64 (pow.f64 k -1/2))) 1)
(*.f64 1 (pow.f64 k -1/2))
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(*.f64 (cbrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 k -1/2)))
(*.f64 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.f64 k) -1/2))
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(log1p.f64 (expm1.f64 (pow.f64 k -1/2)))
(exp.f64 (*.f64 -1/2 (log.f64 k)))
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(+.f64 0 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
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(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 1)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 (sqrt.f64 k) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))
(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4))))
(/.f64 (neg.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 1) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (.f64 -1 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) -1) (neg.f64 (sqrt.f64 k)))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1)
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
(pow.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 k 3/2)) 1/3)
(pow.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)
(pow.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3)) 1/3)
(pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) -1)
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 k 3/2)))
(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 1))
(+.f64 0 (.f64 2 (.f64 (PI.f64) n)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))))
(-.f64 (exp.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n)))) 1)
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1)
(pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3) 1/3)
(pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) 3)
(pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 2)
(pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)) 1/3)
(pow.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)) 1/3)
(sqrt.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2)))
(log.f64 (pow.f64 (exp.f64 n) (*.f64 2 (PI.f64))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 2 (.f64 (PI.f64) n)))))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3))
(cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)))
(cbrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)))
(expm1.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n))))
(log1p.f64 (expm1.f64 (.f64 2 (.f64 (PI.f64) n))))
(exp.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))))
(exp.f64 (.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) 1))

Outputs
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(+.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(+.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) k)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))
(.f64 (+.f64 (.f64 (.f64 k -1/2) (log.f64 (.f64 n (.f64 2 (PI.f64))))) 1) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (+.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(fma.f64 1/2 (.f64 (.f64 k k) (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2))) (+.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(fma.f64 1/2 (.f64 k (.f64 k (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 -1/2 (log.f64 (.f64 n (.f64 2 (PI.f64))))) 2)))) (fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) k)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
(+.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 (.f64 (.f64 1/2 (.f64 k k)) (pow.f64 (.f64 -1/2 (log.f64 (.f64 n (.f64 2 (PI.f64))))) 2)) (.f64 (.f64 k -1/2) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (+.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (+.f64 (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 1/6 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64))))) 3) (pow.f64 k 3)))))))
(fma.f64 1/2 (.f64 (.f64 k k) (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2))) (+.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (fma.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 1/6 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (.f64 -1/8 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (pow.f64 k 3)))))))
(+.f64 (fma.f64 1/2 (.f64 k (.f64 k (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 -1/2 (log.f64 (.f64 n (.f64 2 (PI.f64))))) 2)))) (fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) k)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))) (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (.f64 (.f64 -1/8 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3)) (pow.f64 k 3)) 1/6)))
(+.f64 (.f64 (+.f64 (.f64 (.f64 k -1/2) (log.f64 (.f64 n (.f64 2 (PI.f64))))) 1) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 (.f64 1/6 (.f64 (.f64 -1/8 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3)) (pow.f64 k 3))) (.f64 (.f64 1/2 (.f64 k k)) (pow.f64 (.f64 -1/2 (log.f64 (.f64 n (*.f64 2 (PI.f64))))) 2)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
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(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(cbrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(expm1.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(log1p.f64 (expm1.f64 (.f64 2 (.f64 (PI.f64) n))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(exp.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(exp.f64 (.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) 1))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))

localize23.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
✓	0.2b	(*.f64 (PI.f64) n)
✓	0.3b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))

Compiler

Compiled 50 to 30 computations (40% saved)

series3.3s (3.9%)

Counts

3 → 40

Calls

15 calls:

Time	Variable		Point	Expression
1.2s	k	@	0	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
902.0ms	k	@	inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
869.0ms	k	@	-inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
202.0ms	n	@	-inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
184.0ms	n	@	-inf	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))

Compiler

Compiled 347052 to 259642 computations (25.2% saved)

rewrite66.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

759×	`log-prod_binary64`
385×	`pow2_binary64`
262×	`pow1/3_binary64`
261×	`expm1-udef_binary64`
261×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	295	44
2	3931	40

Stop Event

1×	node limit

Counts

3 → 92

Calls

Call 1

Inputs
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))
(*.f64 (PI.f64) n)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))

Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (PI.f64) n) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) n) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) n) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (PI.f64) n)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (PI.f64) n) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (PI.f64)) n))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (PI.f64) n) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (*.f64 (PI.f64) n)) 1))))))
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Outputs

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(fma.f64 k -1/2 1/2))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))))))

simplify66.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

718×	`fma-def_binary64`
497×	`associate-/l*_binary64`
490×	`unswap-sqr_binary64`
461×	`distribute-rgt-in_binary64`
446×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	272	2833
1	619	2507
2	2252	2475

Stop Event

1×	node limit

Counts

132 → 173

Calls

Call 1

Inputs
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2)
(+.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (+.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (+.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (+.f64 (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 1/6 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64))))) 3) (pow.f64 k 3)))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k)))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k)))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k)))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k)))) (sqrt.f64 k))
(+.f64 0 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))) 1)
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 1)
(.f64 1 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))
(.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)))
(.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (/.f64 1 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 1/2 k))))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 2 (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))
(.f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 2)) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 1 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 1/2 k)) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 k)))
(/.f64 (neg.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (neg.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 k))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))))
(log.f64 (exp.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 n (.f64 2 (PI.f64))))) 1))
(+.f64 0 (*.f64 (PI.f64) n))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) n))) 1)
(pow.f64 (*.f64 (PI.f64) n) 1)
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) 2) 1/2)
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) 3) 1/3)
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 3)
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 2)
(pow.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)) 1/3)
(pow.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)) 1/3)
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) 2))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) n))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) n))))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) 3))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)))
(cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) n)))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) n)))
(exp.f64 (log.f64 (*.f64 (PI.f64) n)))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) n)) 1))
(+.f64 0 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)
(.f64 1 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))) (.f64 (cbrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2))) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2))) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
(.f64 (neg.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k 1/4)))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)
(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k) 1/2)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3) 1/3)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) -1)
(pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)) 1/3)
(pow.f64 (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 1) -1)
(neg.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
(log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))

Outputs
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(+.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(+.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) k)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 (.f64 (.f64 k -1/2) (log.f64 (.f64 n (*.f64 2 (PI.f64))))) 1))
(+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (+.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(fma.f64 1/2 (.f64 (.f64 k k) (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2))) (+.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(fma.f64 1/2 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2) (.f64 k k))) (fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) k)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(+.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 (.f64 (.f64 k -1/2) (log.f64 (.f64 n (.f64 2 (PI.f64))))) (.f64 (.f64 1/2 (.f64 k k)) (pow.f64 (.f64 -1/2 (log.f64 (.f64 n (*.f64 2 (PI.f64))))) 2)))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (+.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (+.f64 (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 1/6 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64))))) 3) (pow.f64 k 3)))))))
(fma.f64 1/2 (.f64 (.f64 k k) (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2))) (+.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (fma.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 1/6 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (.f64 -1/8 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (pow.f64 k 3)))))))
(+.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2) (.f64 k k))) (fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) k)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (.f64 (.f64 (pow.f64 k 3) -1/8) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) 1/6)))
(+.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 (.f64 (.f64 k -1/2) (log.f64 (.f64 n (.f64 2 (PI.f64))))) 1)) (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 (.f64 1/6 (.f64 (.f64 (pow.f64 k 3) -1/8) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3))) (.f64 (.f64 1/2 (.f64 k k)) (pow.f64 (.f64 -1/2 (log.f64 (.f64 n (*.f64 2 (PI.f64))))) 2)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k)))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k)))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k)))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k)))) (sqrt.f64 k))
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(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(/.f64 (exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))
(/.f64 (exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (.f64 n 2) (PI.f64)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(/.f64 (exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(/.f64 (exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(/.f64 (exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))
(/.f64 (exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (*.f64 n 2) (PI.f64))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

eval133.0ms (0.2%)

Compiler: Compiled 7566 to 5130 computations (32.2% saved)

prune83.0ms (0.1%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	321	25	346
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	322	26	348

Error

0.0b

Counts

348 → 26

Alt Table

Click to see full alt table

Status	Error	Program
	10.7b	(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
	11.1b	(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
✓	0.4b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.6b	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
	3.5b	(/.f64 (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
	0.3b	(/.f64 (/.f64 1 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 1/2 k)) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
	22.3b	(/.f64 (+.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))) (sqrt.f64 k))
▶	0.3b	(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 n 2) (PI.f64))) (pow.f64 (.f64 (.f64 n 2) (PI.f64)) (.f64 k -1/2))) (sqrt.f64 k))
	0.4b	(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 k))
▶	22.6b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
	3.4b	(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
▶	0.4b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
	1.0b	(.f64 (pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.5b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 1 (.f64 2 (*.f64 k -1/2)))))
	3.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
▶	0.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 2 (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (*.f64 k 1/2)))))
	22.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
	3.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
	0.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	3.2b	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.2b	(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	10.6b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	12.5b	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
	26.4b	(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)))

Compiler

Compiled 960 to 785 computations (18.2% saved)

localize28.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (sqrt.f64 (.f64 (.f64 n 2) (PI.f64))) (pow.f64 (.f64 (.f64 n 2) (PI.f64)) (.f64 k -1/2)))
✓	0.2b	(sqrt.f64 (.f64 (.f64 n 2) (PI.f64)))
✓	0.2b	(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 n 2) (PI.f64))) (pow.f64 (.f64 (.f64 n 2) (PI.f64)) (.f64 k -1/2))) (sqrt.f64 k))
✓	0.2b	(.f64 (.f64 n 2) (PI.f64))

Compiler

Compiled 70 to 46 computations (34.3% saved)

series7.8s (9.2%)

Counts

4 → 24

Calls

18 calls:

Time	Variable		Point	Expression
920.0ms	k	@	-inf	(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 n 2) (PI.f64))) (pow.f64 (.f64 (.f64 n 2) (PI.f64)) (.f64 k -1/2))) (sqrt.f64 k))
918.0ms	k	@	inf	(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 n 2) (PI.f64))) (pow.f64 (.f64 (.f64 n 2) (PI.f64)) (.f64 k -1/2))) (sqrt.f64 k))
908.0ms	k	@	0	(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 n 2) (PI.f64))) (pow.f64 (.f64 (.f64 n 2) (PI.f64)) (.f64 k -1/2))) (sqrt.f64 k))
749.0ms	n	@	inf	(.f64 (sqrt.f64 (.f64 (.f64 n 2) (PI.f64))) (pow.f64 (.f64 (.f64 n 2) (PI.f64)) (.f64 k -1/2)))
703.0ms	n	@	inf	(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 n 2) (PI.f64))) (pow.f64 (.f64 (.f64 n 2) (PI.f64)) (.f64 k -1/2))) (sqrt.f64 k))

Compiler

Compiled 921770 to 661320 computations (28.3% saved)

rewrite70.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

807×	`log-prod_binary64`
693×	`pow-unpow_binary64`
378×	`pow2_binary64`
260×	`pow1/3_binary64`
256×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	75
1	298	57
2	3806	53

Stop Event

1×	node limit

Counts

4 → 121

Calls

Call 1

Inputs
(.f64 (.f64 n 2) (PI.f64))
(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 n 2) (PI.f64))) (pow.f64 (.f64 (.f64 n 2) (PI.f64)) (.f64 k -1/2))) (sqrt.f64 k))
(sqrt.f64 (.f64 (.f64 n 2) (PI.f64)))
(.f64 (sqrt.f64 (.f64 (.f64 n 2) (PI.f64))) (pow.f64 (.f64 (.f64 n 2) (PI.f64)) (.f64 k -1/2)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 n (.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 n (.f64 2 (PI.f64))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 n (.f64 2 (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 n (.f64 2 (PI.f64)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 n (.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 n (.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 n (.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 2) (.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) 1) (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) 1) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2) (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) 3) (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2) (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) 3) (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 n (.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 n (.f64 2 (PI.f64))))) 1))))))

simplify69.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

421×	`associate-/r*_binary64`
280×	`associate-/l/_binary64`
272×	`log-prod_binary64`
224×	`associate-r_binary64`
220×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	300	3123
1	669	3033
2	3043	2514

Stop Event

1×	node limit

Counts

145 → 168

Calls

Call 1

Inputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 1/2 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (pow.f64 k 2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64))))) 2))))))
(+.f64 (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (pow.f64 k 2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (.f64 1/6 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64))))) 3) (pow.f64 k 3)))))))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(+.f64 0 (.f64 n (.f64 2 (PI.f64))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))))
(-.f64 (exp.f64 (log1p.f64 (.f64 n (.f64 2 (PI.f64))))) 1)
(pow.f64 (.f64 n (.f64 2 (PI.f64))) 1)
(pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) 2)
(pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 2) 1/2)
(pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3) 1/3)
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (PI.f64)))) 3)
(pow.f64 (*.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)) 1/3)
(pow.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)) 1/3)
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 2))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 n (.f64 2 (PI.f64))))))
(cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3))
(cbrt.f64 (*.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)))
(expm1.f64 (log1p.f64 (.f64 n (.f64 2 (PI.f64)))))
(log1p.f64 (expm1.f64 (.f64 n (.f64 2 (PI.f64)))))
(exp.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(exp.f64 (.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 1))
(+.f64 0 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)
(.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)))))
(.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 k -1/2)) (pow.f64 k -1/2)))
(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (pow.f64 k -1/2)))
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)
(.f64 1 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 2) (.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
(.f64 (neg.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) 1) (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) 1) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (cbrt.f64 k)) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 2) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (pow.f64 k 1/4)))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k 1/4)))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 2) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k 1/4)))
(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)
(pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2) k) 1/2)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3) 1/3)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) -1)
(pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)) 1/3)
(pow.f64 (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 1) -1)
(neg.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2) k))
(log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))
(+.f64 0 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))) 1)
(.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) 1)
(.f64 1 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
(.f64 (cbrt.f64 (.f64 n (.f64 2 (PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (cbrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n)))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 2 (PI.f64))))
(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 1/4) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) 1/4))
(*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 n (.f64 2 (PI.f64)))) 2)) (sqrt.f64 (cbrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) 1/2)
(pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) 1)
(pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) 3)
(pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 1/4) 2)
(fabs.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))))
(cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))) 1))
(+.f64 0 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))) 1)
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 1)
(pow.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2) 1/2)
(pow.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3) 1/3)
(pow.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 3)
(pow.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 2)
(pow.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2) (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) 3)) 1/3)
(pow.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) 3) (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2)) 1/3)
(sqrt.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2))
(log.f64 (exp.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3))
(cbrt.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2) (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) 3) (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2)))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 n (.f64 2 (PI.f64))))) 1))

Outputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(fma.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(fma.f64 -1/2 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(+.f64 (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 1/2 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (pow.f64 k 2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64))))) 2))))))
(+.f64 (fma.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (.f64 1/2 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (.f64 k k) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64))))) 2)))))
(fma.f64 -1/2 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) (fma.f64 1/2 (.f64 (.f64 k k) (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(+.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (+.f64 (.f64 1/2 (.f64 (.f64 k k) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2))) (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(+.f64 (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (pow.f64 k 2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (.f64 1/6 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64))))) 3) (pow.f64 k 3)))))))
(+.f64 (fma.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (fma.f64 1/2 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (.f64 k k) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2))) (.f64 1/6 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (.f64 -1/8 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (pow.f64 k 3))))))
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(.f64 (pow.f64 (exp.f64 (.f64 -1/2 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 1)
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 (.f64 -1/2 k) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (pow.f64 (exp.f64 (.f64 -1/2 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2) 1/2)
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 (.f64 -1/2 k) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (pow.f64 (exp.f64 (.f64 -1/2 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3) 1/3)
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 (.f64 -1/2 k) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (pow.f64 (exp.f64 (.f64 -1/2 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 3)
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 (.f64 -1/2 k) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (pow.f64 (exp.f64 (.f64 -1/2 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 2)
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 (.f64 -1/2 k) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (pow.f64 (exp.f64 (.f64 -1/2 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2) (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) 3)) 1/3)
(cbrt.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2) (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 -1/2 k)) 3)))
(cbrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 -1/2 k)) 3)))
(pow.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) 3) (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2)) 1/3)
(cbrt.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2) (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 -1/2 k)) 3)))
(cbrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 -1/2 k)) 3)))
(sqrt.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 (.f64 -1/2 k) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (pow.f64 (exp.f64 (.f64 -1/2 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(log.f64 (exp.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 (.f64 -1/2 k) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (pow.f64 (exp.f64 (.f64 -1/2 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 (.f64 -1/2 k) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (pow.f64 (exp.f64 (.f64 -1/2 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 (.f64 -1/2 k) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (pow.f64 (exp.f64 (.f64 -1/2 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(cbrt.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2) (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) 3)))
(cbrt.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2) (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 -1/2 k)) 3)))
(cbrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 -1/2 k)) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) 3) (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2)))
(cbrt.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2) (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 -1/2 k)) 3)))
(cbrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 -1/2 k)) 3)))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 (.f64 -1/2 k) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (pow.f64 (exp.f64 (.f64 -1/2 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 (.f64 -1/2 k) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (pow.f64 (exp.f64 (.f64 -1/2 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 (.f64 -1/2 k) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (pow.f64 (exp.f64 (.f64 -1/2 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 n (.f64 2 (PI.f64))))) 1))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 (.f64 -1/2 k) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (pow.f64 (exp.f64 (.f64 -1/2 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))

localize15.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
✓	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	0.4b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))

Compiler

Compiled 31 to 19 computations (38.7% saved)

series4.3s (5.1%)

Counts

3 → 12

Calls

12 calls:

Time	Variable		Point	Expression
700.0ms	k	@	0	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
660.0ms	k	@	-inf	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
617.0ms	k	@	inf	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
418.0ms	n	@	inf	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
409.0ms	n	@	-inf	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))

Compiler

Compiled 434528 to 303956 computations (30% saved)

rewrite60.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

546×	`log-prod_binary64`
400×	`exp-prod_binary64`
327×	`pow-prod-down_binary64`
254×	`pow2_binary64`
210×	`pow-unpow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	208	31
2	2616	31

Stop Event

1×	node limit

Counts

3 → 129

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
(.f64 n (.f64 2 (PI.f64)))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))

Outputs

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k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/6) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 n) 1) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (cbrt.f64 k)) (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 n) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 k 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(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3/2) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/4)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2))))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 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(sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 1) (*.f64 (log.f64 (sqrt.f64 k)) 1)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (PI.f64) (*.f64 n 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (*.f64 2 (PI.f64)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (*.f64 2 (PI.f64))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3/2) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/6) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 2)) (cbrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))) (sqrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 n) (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 1) 2))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/6) (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n 2)) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/2) (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 1) 1))))))

simplify57.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

549×	`associate-/l*_binary64`
525×	`fma-def_binary64`
376×	`distribute-rgt-in_binary64`
360×	`distribute-lft-in_binary64`
338×	`times-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	306	1848
1	655	1787
2	2013	1787

Stop Event

1×	node limit

Counts

141 → 182

Calls

Call 1

Inputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(+.f64 0 (sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))))) 1)
(.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))) 1)
(.f64 1 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/6) (pow.f64 k -1/2)))
(.f64 (pow.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)) 1/6) (cbrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))))
(.f64 (cbrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))) (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/6))
(.f64 (sqrt.f64 n) (.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 k -1/2)))
(.f64 (pow.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)) 1/4) (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/4))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/4) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/4) (pow.f64 k -1/2)))
(.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2)))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))))
(.f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 1) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) 1/6) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 n) 1) (/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/4) 1) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) 1/4) (sqrt.f64 k)))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k 1/6)))
(.f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) (cbrt.f64 k)) (pow.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)) 1/6))
(.f64 (/.f64 (sqrt.f64 n) (cbrt.f64 k)) (/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 k 1/6)))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/4) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) 1/4) (pow.f64 k 1/6)))
(.f64 (pow.f64 k -1/4) (/.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k 1/4)))
(.f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) 1/6) (pow.f64 k 1/4)))
(.f64 (/.f64 (sqrt.f64 n) (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 k 1/4)))
(pow.f64 (sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))) 1)
(pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/2)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2) 1/3)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/6) 3)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/4) 2)
(pow.f64 (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 n 2)))) -1)
(pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))))
(pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3/2) (pow.f64 k 3/2)) 1/3)
(pow.f64 (/.f64 (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 n 2)))) 1) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)))))) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))))))
(neg.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (neg.f64 (sqrt.f64 k))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))))))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2))
(cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3/2) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)))) 1))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))) 1/2))
(exp.f64 (.f64 (log.f64 (pow.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)) 3/2)) 1/3))
(exp.f64 (.f64 (log.f64 (pow.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)) 1/6)) 3))
(exp.f64 (.f64 (log.f64 (pow.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)) 1/4)) 2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 k (.f64 (PI.f64) (*.f64 n 2))))) -1))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))) 1) 1))
(exp.f64 (-.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 n 2))) 1/2) (log.f64 (sqrt.f64 k))))
(exp.f64 (-.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2)))) 1) (log.f64 (sqrt.f64 k))))
(exp.f64 (-.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (*.f64 (log.f64 k) 1/2)))
(exp.f64 (-.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 1/2) (.f64 (log.f64 k) 1/2)))
(exp.f64 (-.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) 1) (.f64 (log.f64 k) 1/2)))
(exp.f64 (-.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (*.f64 (log.f64 (sqrt.f64 k)) 1)))
(exp.f64 (-.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 1/2) (.f64 (log.f64 (sqrt.f64 k)) 1)))
(exp.f64 (-.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) 1) (.f64 (log.f64 (sqrt.f64 k)) 1)))
(+.f64 0 (.f64 (PI.f64) (.f64 n 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) (.f64 n 2)))) 1)
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1)
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 2)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 2) 1/2)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3) 1/3)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3/2) 2/3)
(pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 3)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/6) 6)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/4) 4)
(pow.f64 (exp.f64 1) (log.f64 (.f64 (PI.f64) (.f64 n 2))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2)))) 2)) (cbrt.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))))) (sqrt.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2)))))
(sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 2))
(log.f64 (pow.f64 (exp.f64 n) (*.f64 2 (PI.f64))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (PI.f64) (.f64 n 2)))))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3))
(expm1.f64 (log1p.f64 (.f64 (PI.f64) (.f64 n 2))))
(log1p.f64 (expm1.f64 (.f64 (PI.f64) (.f64 n 2))))
(exp.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 n 2))) 1))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2)))) 2))
(exp.f64 (.f64 (.f64 2 (log.f64 (.f64 (PI.f64) (.f64 n 2)))) 1/2))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) 3)) 1/3))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 n 2)))) 3))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 1) 1))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 1/2) 2))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) 1) 2))
(+.f64 0 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))) 1)
(.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) 1)
(.f64 1 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) 1/6))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/6) (cbrt.f64 (.f64 (PI.f64) (*.f64 n 2))))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 n))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 2 (PI.f64))))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/4) (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) 1/4))
(.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (PI.f64)))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/2)
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 1)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 2) 1/4)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3) 1/6)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3/2) 1/3)
(pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 3/2)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/6) 3)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/4) 2)
(pow.f64 (exp.f64 1/2) (log.f64 (.f64 (PI.f64) (.f64 n 2))))
(pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))))
(fabs.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 n 2))) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2)))) 1))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) 3/2)) 1/3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) 1/6)) 3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) 1/4)) 2))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 1) 1/2))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 1/2) 1))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) 1) 1))

Outputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(+.f64 0 (sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)))))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) (/.f64 k 2))))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 n (*.f64 (/.f64 2 k) (PI.f64))))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) (/.f64 k 2))))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 n (*.f64 (/.f64 2 k) (PI.f64))))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))))) 1)
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k -1/2))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))) 1)
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(.f64 1 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/6) (pow.f64 k -1/2)))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(.f64 (pow.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)) 1/6) (cbrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(.f64 (cbrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))) (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/6))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(.f64 (sqrt.f64 n) (.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 k -1/2)))
(.f64 (sqrt.f64 n) (.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (PI.f64)))))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (*.f64 (pow.f64 k -1/2) (sqrt.f64 n)))
(.f64 (pow.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)) 1/4) (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/4))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/4) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/4) (pow.f64 k -1/2)))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2)))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(.f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 1) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) 1/6) (sqrt.f64 k)))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(.f64 (/.f64 (sqrt.f64 n) 1) (/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))
(.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (sqrt.f64 (.f64 2 (PI.f64))))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/4) 1) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) 1/4) (sqrt.f64 k)))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k 1/6)))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k 1/6)))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 k 1/6)) (cbrt.f64 k))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (*.f64 (cbrt.f64 k) (pow.f64 k 1/6)))
(.f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) (cbrt.f64 k)) (pow.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)) 1/6))
(.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/6) (/.f64 (cbrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 k)))
(.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) (/.f64 k 2))) 1/6) (/.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n))) (cbrt.f64 k)))
(/.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (/.f64 (cbrt.f64 k) (pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 1/6)))
(.f64 (/.f64 (sqrt.f64 n) (cbrt.f64 k)) (/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 k 1/6)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (/.f64 (sqrt.f64 n) (cbrt.f64 k))) (pow.f64 k 1/6))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/4) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) 1/4) (pow.f64 k 1/6)))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k 1/6)))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 k 1/6)) (cbrt.f64 k))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (*.f64 (cbrt.f64 k) (pow.f64 k 1/6)))
(.f64 (pow.f64 k -1/4) (/.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k 1/4)))
(.f64 (pow.f64 k -1/4) (/.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k 1/4)))
(.f64 (pow.f64 k -1/4) (/.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))) (pow.f64 k 1/4)))
(.f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) 1/6) (pow.f64 k 1/4)))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(.f64 (/.f64 (sqrt.f64 n) (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 k 1/4)))
(.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))
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(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) 1/6))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/6) (cbrt.f64 (.f64 (PI.f64) (*.f64 n 2))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 n))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 2 (PI.f64))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 2 (PI.f64))))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/4) (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) 1/4))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (PI.f64)))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/2)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 1)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 2) 1/4)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3) 1/6)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3/2) 1/3)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 3/2)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/6) 3)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/4) 2)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(pow.f64 (exp.f64 1/2) (log.f64 (.f64 (PI.f64) (.f64 n 2))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))))))
(fabs.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(log.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3/2))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(exp.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 n 2))) 1/2))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2)))) 1))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) 3/2)) 1/3))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) 1/6)) 3))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) 1/4)) 2))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 1) 1/2))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 1/2) 1))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) 1) 1))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))

localize28.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
✓	0.2b	(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
	0.2b	(*.f64 (PI.f64) n)
✓	0.2b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))

Compiler

Compiled 67 to 38 computations (43.3% saved)

series5.9s (7%)

Counts

3 → 36

Calls

18 calls:

Time	Variable		Point	Expression
1.4s	k	@	0	(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
1.2s	k	@	0	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
905.0ms	k	@	-inf	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
883.0ms	k	@	inf	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
541.0ms	k	@	-inf	(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))

Compiler

Compiled 737224 to 526416 computations (28.6% saved)

rewrite69.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

769×	`log-prod_binary64`
379×	`pow2_binary64`
261×	`pow1/3_binary64`
257×	`expm1-udef_binary64`
256×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	55
1	307	52
2	4016	52

Stop Event

1×	node limit

Counts

3 → 122

Calls

Call 1

Inputs

(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))

(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))

(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))

Outputs

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simplify81.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

750×	`fma-def_binary64`
543×	`unswap-sqr_binary64`
502×	`times-frac_binary64`
481×	`distribute-rgt-in_binary64`
194×	`log-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	330	4122
1	782	3623
2	2832	3607

Stop Event

1×	node limit

Counts

158 → 240

Calls

Call 1

Inputs
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(.f64 2 (.f64 n (PI.f64)))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 2 (.f64 n (PI.f64))))
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(.f64 (/.f64 1 (cbrt.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))
(.f64 (.f64 (pow.f64 k -1/2) 1) (sqrt.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))))
(.f64 (.f64 (pow.f64 k -1/2) (cbrt.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)))) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)))))
(.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) 1/4)) (pow.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) 1/4))
(pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)))) -1)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) 1)
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) 3) 1/3)
(pow.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))) -1/2)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))) 2)
(pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)) 1/3)
(pow.f64 (neg.f64 (neg.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)))))) -1)
(pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) 1/4) (pow.f64 k 1/4)) 2)
(sqrt.f64 (/.f64 1 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k))))) -1))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k))) 1))

Outputs
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 2 (.f64 n (PI.f64))))
(fma.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 2 (*.f64 n (PI.f64))))
(fma.f64 2 (.f64 n (PI.f64)) (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(.f64 n (+.f64 (.f64 (.f64 k -2) (.f64 (PI.f64) (log.f64 (.f64 n (.f64 2 (PI.f64)))))) (*.f64 2 (PI.f64))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 n (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 -1 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2) (PI.f64)))) (.f64 2 (.f64 n (PI.f64)))))
(fma.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (fma.f64 n (.f64 (.f64 k k) (.f64 (PI.f64) (pow.f64 (neg.f64 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2))) (.f64 2 (.f64 n (PI.f64)))))
(fma.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (fma.f64 n (.f64 (PI.f64) (.f64 k (.f64 k (pow.f64 (neg.f64 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (.f64 2 (.f64 n (PI.f64)))))
(fma.f64 k (.f64 (.f64 (PI.f64) (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) n)) -2) (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 k (.f64 k (pow.f64 (neg.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64))))) 2))) 2)))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 1/3 (.f64 n (.f64 (pow.f64 (.f64 -1 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 3) (.f64 (pow.f64 k 3) (PI.f64))))) (+.f64 (.f64 n (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 -1 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2) (PI.f64)))) (.f64 2 (*.f64 n (PI.f64))))))
(fma.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (fma.f64 1/3 (.f64 n (.f64 (pow.f64 (neg.f64 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 3) (.f64 (PI.f64) (pow.f64 k 3)))) (fma.f64 n (.f64 (.f64 k k) (.f64 (PI.f64) (pow.f64 (neg.f64 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2))) (.f64 2 (*.f64 n (PI.f64))))))
(fma.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (fma.f64 1/3 (.f64 (pow.f64 (neg.f64 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 3) (.f64 (.f64 (PI.f64) (pow.f64 k 3)) n)) (fma.f64 n (.f64 (PI.f64) (.f64 k (.f64 k (pow.f64 (neg.f64 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (.f64 2 (*.f64 n (PI.f64))))))
(fma.f64 k (.f64 (.f64 (PI.f64) (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) n)) -2) (fma.f64 n (.f64 (.f64 (PI.f64) (.f64 (neg.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3)) (pow.f64 k 3))) 1/3) (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 k (.f64 k (pow.f64 (neg.f64 (log.f64 (.f64 n (.f64 2 (PI.f64))))) 2))) 2))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(/.f64 (sqrt.f64 k) (sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
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(/.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
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(/.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
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(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 1 (/.f64 k (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k))))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))) (cbrt.f64 (.f64 (/.f64 1 k) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(.f64 (cbrt.f64 (/.f64 1 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))) (cbrt.f64 (.f64 (/.f64 1 k) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))) (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)))))))
(/.f64 -1 (neg.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k))))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (pow.f64 k -1/2))
(.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) -1/2)))
(/.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) -1/2))
(/.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) -1/2))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))) 1) (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) 1/4) 1) (/.f64 (pow.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) 1/4) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))) (cbrt.f64 k)) (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 k)) (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (cbrt.f64 k)) (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) 1/4) (cbrt.f64 k)) (/.f64 (pow.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) 1/4) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k))) (pow.f64 k 1/4)))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (pow.f64 k 1/4)))
(/.f64 1 (/.f64 (pow.f64 k 1/2) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (/.f64 1 (sqrt.f64 k)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)))) (pow.f64 k 1/4)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) (pow.f64 k 1/4)))
(/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (/.f64 (pow.f64 k 1/4) (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))) (pow.f64 k 1/4))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) (pow.f64 k 1/4)))
(.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) 1/4) (pow.f64 k 1/4)) (/.f64 (pow.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) 1/4) (pow.f64 k 1/4)))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (pow.f64 k 1/4)))
(/.f64 1 (/.f64 (pow.f64 k 1/2) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (/.f64 1 (sqrt.f64 k)))
(.f64 (/.f64 1 (neg.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)))))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (pow.f64 k 1/4)))
(/.f64 1 (/.f64 (pow.f64 k 1/2) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (/.f64 1 (sqrt.f64 k)))
(.f64 (/.f64 1 (cbrt.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))) (/.f64 1 (cbrt.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))))
(/.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(/.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(.f64 (.f64 (pow.f64 k -1/2) 1) (sqrt.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (pow.f64 k -1/2))
(.f64 (.f64 (pow.f64 k -1/2) (cbrt.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)))) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)))))
(.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))) (.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (pow.f64 k -1/2)))
(.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))) (.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (pow.f64 k -1/2)))
(.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) 1/4)) (pow.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) 1/4))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (pow.f64 k -1/2))
(pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)))) -1)
(/.f64 -1 (neg.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) 1)
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) 3) 1/3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))) -1/2)
(pow.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) -1/2)
(pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) -1/2)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))) 3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))) 2)
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)) 1/3)
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)))
(pow.f64 (neg.f64 (neg.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)))))) -1)
(/.f64 -1 (neg.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) 1/4) (pow.f64 k 1/4)) 2)
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (pow.f64 k 1/4)))
(/.f64 1 (/.f64 (pow.f64 k 1/2) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (/.f64 1 (sqrt.f64 k)))
(sqrt.f64 (/.f64 1 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k)))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) 3))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k))))) -1))
(/.f64 -1 (neg.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k))) 1))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))

localize37.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
	0.3b	(/.f64 1 (sqrt.f64 k))
✓	0.3b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (.f64 k 1/2))))
✓	0.6b	(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2)))

Compiler

Compiled 80 to 58 computations (27.5% saved)

series5.4s (6.4%)

Counts

3 → 40

Calls

15 calls:

Time	Variable		Point	Expression
2.1s	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
1.4s	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
1.1s	k	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
428.0ms	n	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
299.0ms	n	@	-inf	(.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (.f64 k 1/2))))

Compiler

Compiled 503990 to 402695 computations (20.1% saved)

rewrite74.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

884×	`log-prod_binary64`
296×	`expm1-udef_binary64`
296×	`log1p-udef_binary64`
290×	`log-pow_binary64`
185×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	53
1	353	53
2	4575	47

Stop Event

1×	node limit

Counts

3 → 88

Calls

Call 1

Inputs

(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 k 1/2)))

(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2))))

(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))) (cbrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 1/2 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 n)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (PI.f64))) k) (pow.f64 (sqrt.f64 n) k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 2 (PI.f64)))) (*.f64 (pow.f64 (sqrt.f64 n) k) (pow.f64 (sqrt.f64 (*.f64 2 (PI.f64))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (fma.f64 k -1/2 1/2))) (pow.f64 (sqrt.f64 (*.f64 2 (PI.f64))) k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 n) (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (pow.f64 (sqrt.f64 n) k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 n)) (pow.f64 (sqrt.f64 n) k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (*.f64 2 (PI.f64)))) (pow.f64 (sqrt.f64 (*.f64 2 (PI.f64))) k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (pow.f64 (cbrt.f64 (fma.f64 k -1/2 1/2)) 2)) (cbrt.f64 (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 (fma.f64 k -1/2 1/2))) (sqrt.f64 (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) 3) (pow.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (fma.f64 k -1/2 1/2)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 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(#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 2) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 (pow.f64 k -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))))))

simplify81.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

590×	`distribute-rgt-in_binary64`
576×	`distribute-lft-in_binary64`
291×	`associate-r_binary64`
232×	`associate-/l/_binary64`
227×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	316	3550
1	803	3385
2	3313	2856

Stop Event

1×	node limit

Counts

128 → 168

Calls

Call 1

Inputs
(pow.f64 (*.f64 2 (PI.f64)) 1/2)
(+.f64 (.f64 -1/2 (.f64 k (.f64 (log.f64 (.f64 2 (PI.f64))) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (pow.f64 (.f64 2 (PI.f64)) 1/2))
(+.f64 (.f64 -1/2 (.f64 k (.f64 (log.f64 (.f64 2 (PI.f64))) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (+.f64 (.f64 1/2 (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (PI.f64)))) 2) (.f64 (pow.f64 k 2) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (pow.f64 (.f64 2 (PI.f64)) 1/2)))
(+.f64 (.f64 1/6 (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (PI.f64)))) 3) (.f64 (pow.f64 (.f64 2 (PI.f64)) 1/2) (pow.f64 k 3)))) (+.f64 (.f64 -1/2 (.f64 k (.f64 (log.f64 (.f64 2 (PI.f64))) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (+.f64 (.f64 1/2 (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (PI.f64)))) 2) (.f64 (pow.f64 k 2) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (pow.f64 (.f64 2 (PI.f64)) 1/2))))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(.f64 (pow.f64 n 1/2) (pow.f64 (.f64 2 (PI.f64)) 1/2))
(+.f64 (.f64 (pow.f64 n 1/2) (pow.f64 (.f64 2 (PI.f64)) 1/2)) (.f64 k (+.f64 (.f64 -1/2 (.f64 (pow.f64 n 1/2) (.f64 (log.f64 n) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (.f64 -1/2 (.f64 (pow.f64 n 1/2) (.f64 (log.f64 (.f64 2 (PI.f64))) (pow.f64 (.f64 2 (PI.f64)) 1/2)))))))
(+.f64 (.f64 (+.f64 (.f64 1/2 (.f64 (pow.f64 n 1/2) (.f64 (pow.f64 (.f64 -1/2 (log.f64 n)) 2) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (+.f64 (.f64 1/2 (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (PI.f64)))) 2) (.f64 (pow.f64 n 1/2) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (.f64 1/4 (.f64 (pow.f64 n 1/2) (.f64 (pow.f64 (.f64 2 (PI.f64)) 1/2) (.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))) (pow.f64 k 2)) (+.f64 (.f64 (pow.f64 n 1/2) (pow.f64 (.f64 2 (PI.f64)) 1/2)) (.f64 k (+.f64 (.f64 -1/2 (.f64 (pow.f64 n 1/2) (.f64 (log.f64 n) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (.f64 -1/2 (.f64 (pow.f64 n 1/2) (.f64 (log.f64 (.f64 2 (PI.f64))) (pow.f64 (.f64 2 (PI.f64)) 1/2))))))))
(+.f64 (.f64 (+.f64 (.f64 1/2 (.f64 (pow.f64 n 1/2) (.f64 (pow.f64 (.f64 -1/2 (log.f64 n)) 2) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (+.f64 (.f64 1/2 (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (PI.f64)))) 2) (.f64 (pow.f64 n 1/2) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (.f64 1/4 (.f64 (pow.f64 n 1/2) (.f64 (pow.f64 (.f64 2 (PI.f64)) 1/2) (.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))) (pow.f64 k 2)) (+.f64 (.f64 (+.f64 (.f64 -1/4 (.f64 (pow.f64 n 1/2) (.f64 (pow.f64 (.f64 -1/2 (log.f64 n)) 2) (.f64 (pow.f64 (.f64 2 (PI.f64)) 1/2) (log.f64 (.f64 2 (PI.f64))))))) (+.f64 (.f64 1/6 (.f64 (pow.f64 n 1/2) (.f64 (pow.f64 (.f64 -1/2 (log.f64 n)) 3) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (+.f64 (.f64 1/6 (.f64 (pow.f64 n 1/2) (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (PI.f64)))) 3) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (.f64 -1/4 (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (PI.f64)))) 2) (.f64 (pow.f64 n 1/2) (.f64 (pow.f64 (.f64 2 (PI.f64)) 1/2) (log.f64 n)))))))) (pow.f64 k 3)) (+.f64 (.f64 (pow.f64 n 1/2) (pow.f64 (.f64 2 (PI.f64)) 1/2)) (.f64 k (+.f64 (.f64 -1/2 (.f64 (pow.f64 n 1/2) (.f64 (log.f64 n) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (.f64 -1/2 (.f64 (pow.f64 n 1/2) (.f64 (log.f64 (.f64 2 (PI.f64))) (pow.f64 (.f64 2 (PI.f64)) 1/2)))))))))
(.f64 (pow.f64 n (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k))))
(.f64 (pow.f64 n (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k))))
(.f64 (pow.f64 n (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k))))
(.f64 (pow.f64 n (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
(.f64 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k))))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k))))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k))))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k))))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))))
(/.f64 (.f64 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))))) (sqrt.f64 k))
(/.f64 (.f64 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))))) (sqrt.f64 k))
(/.f64 (.f64 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))))) (sqrt.f64 k))
(/.f64 (.f64 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))))) (sqrt.f64 k))
(/.f64 (.f64 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k))))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))) (sqrt.f64 k))
(/.f64 (.f64 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k))))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))) (sqrt.f64 k))
(/.f64 (.f64 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k))))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))) (sqrt.f64 k))
(/.f64 (.f64 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k))))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))) (sqrt.f64 k))
(+.f64 0 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))) (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))) 1)
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 1)
(.f64 1 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (.f64 2 (PI.f64)) (.f64 k -1/2)))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (/.f64 1 (pow.f64 (sqrt.f64 (*.f64 2 (PI.f64))) k)))
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)))
(*.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (pow.f64 2 (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))
(.f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 2 (PI.f64))) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(/.f64 1 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) k) (sqrt.f64 (.f64 2 (PI.f64)))))
(/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) k))
(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (PI.f64)))) (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) k)))
(sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2))))
(log.f64 (exp.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))))
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 3))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (PI.f64)))))
(exp.f64 (.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 2 (PI.f64)))) 1))
(+.f64 0 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))
(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))) (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))) 1)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 n)) (.f64 (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) k) (pow.f64 (sqrt.f64 n) k)))
(/.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 2 (PI.f64)))) (.f64 (pow.f64 (sqrt.f64 n) k) (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (fma.f64 k -1/2 1/2))) (pow.f64 (sqrt.f64 (*.f64 2 (PI.f64))) k))
(/.f64 (.f64 (sqrt.f64 n) (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (pow.f64 (sqrt.f64 n) k))
(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 n)) (pow.f64 (sqrt.f64 n) k))
(/.f64 (.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (.f64 2 (PI.f64)))) (pow.f64 (sqrt.f64 (*.f64 2 (PI.f64))) k))
(pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 1)
(pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 3) 1/3)
(pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 3)
(pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 2)
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
(pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (pow.f64 (cbrt.f64 (fma.f64 k -1/2 1/2)) 2)) (cbrt.f64 (fma.f64 k -1/2 1/2)))
(pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 (fma.f64 k -1/2 1/2))) (sqrt.f64 (fma.f64 k -1/2 1/2)))
(sqrt.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 2))
(log.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 3))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) 3) (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 3)))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))
(exp.f64 (log.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 1))
(exp.f64 (.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) (fma.f64 k -1/2 1/2)))
(+.f64 0 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))
(/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))
(/.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 2)) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))
(/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 1) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (.f64 -1 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (neg.f64 (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) -1) (neg.f64 (sqrt.f64 k)))
(/.f64 (.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) (sqrt.f64 n)) (pow.f64 (sqrt.f64 n) k))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3) 1/3)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 2) k))
(log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 3)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))

Outputs
(pow.f64 (*.f64 2 (PI.f64)) 1/2)
(sqrt.f64 (*.f64 2 (PI.f64)))
(+.f64 (.f64 -1/2 (.f64 k (.f64 (log.f64 (.f64 2 (PI.f64))) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (pow.f64 (.f64 2 (PI.f64)) 1/2))
(fma.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 2 (PI.f64)))) (sqrt.f64 (*.f64 2 (PI.f64))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 k (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (*.f64 2 (PI.f64))))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (+.f64 1 (.f64 (.f64 -1/2 k) (log.f64 (*.f64 2 (PI.f64))))))
(+.f64 (.f64 -1/2 (.f64 k (.f64 (log.f64 (.f64 2 (PI.f64))) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (+.f64 (.f64 1/2 (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (PI.f64)))) 2) (.f64 (pow.f64 k 2) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (pow.f64 (.f64 2 (PI.f64)) 1/2)))
(fma.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 2 (PI.f64)))) (fma.f64 1/2 (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (PI.f64)))) 2) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 k k))) (sqrt.f64 (*.f64 2 (PI.f64)))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 k (log.f64 (.f64 2 (PI.f64))))) (fma.f64 (.f64 1/2 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (PI.f64)))) 2)) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 k k)) (sqrt.f64 (*.f64 2 (PI.f64)))))
(+.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (+.f64 (.f64 (.f64 -1/2 k) (log.f64 (.f64 2 (PI.f64)))) (.f64 1/2 (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (PI.f64)))) 2) (*.f64 k k))))))
(+.f64 (.f64 1/6 (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (PI.f64)))) 3) (.f64 (pow.f64 (.f64 2 (PI.f64)) 1/2) (pow.f64 k 3)))) (+.f64 (.f64 -1/2 (.f64 k (.f64 (log.f64 (.f64 2 (PI.f64))) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (+.f64 (.f64 1/2 (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (PI.f64)))) 2) (.f64 (pow.f64 k 2) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (pow.f64 (.f64 2 (PI.f64)) 1/2))))
(fma.f64 1/6 (.f64 (.f64 -1/8 (pow.f64 (log.f64 (.f64 2 (PI.f64))) 3)) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 k 3))) (fma.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 2 (PI.f64)))) (fma.f64 1/2 (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (PI.f64)))) 2) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 k k))) (sqrt.f64 (.f64 2 (PI.f64))))))
(fma.f64 (.f64 -1/48 (pow.f64 (log.f64 (.f64 2 (PI.f64))) 3)) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 k 3)) (fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 k (log.f64 (.f64 2 (PI.f64))))) (fma.f64 (.f64 1/2 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (PI.f64)))) 2)) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 k k)) (sqrt.f64 (*.f64 2 (PI.f64))))))
(+.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (+.f64 (.f64 (.f64 -1/2 k) (log.f64 (.f64 2 (PI.f64)))) (.f64 1/2 (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (PI.f64)))) 2) (.f64 k k))))) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (+.f64 1 (.f64 (.f64 -1/48 (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 3)) (pow.f64 k 3)))))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(.f64 (pow.f64 n 1/2) (pow.f64 (.f64 2 (PI.f64)) 1/2))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 n))
(+.f64 (.f64 (pow.f64 n 1/2) (pow.f64 (.f64 2 (PI.f64)) 1/2)) (.f64 k (+.f64 (.f64 -1/2 (.f64 (pow.f64 n 1/2) (.f64 (log.f64 n) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (.f64 -1/2 (.f64 (pow.f64 n 1/2) (.f64 (log.f64 (.f64 2 (PI.f64))) (pow.f64 (.f64 2 (PI.f64)) 1/2)))))))
(fma.f64 (sqrt.f64 n) (sqrt.f64 (.f64 2 (PI.f64))) (.f64 k (.f64 -1/2 (+.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (log.f64 n))) (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (log.f64 (.f64 2 (PI.f64)))) (sqrt.f64 n))))))
(fma.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 n) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (+.f64 (.f64 (sqrt.f64 n) (log.f64 n)) (.f64 (log.f64 (.f64 2 (PI.f64))) (sqrt.f64 n)))) k)))
(fma.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 n) (.f64 (.f64 k (.f64 -1/2 (sqrt.f64 n))) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))
(+.f64 (.f64 (+.f64 (.f64 1/2 (.f64 (pow.f64 n 1/2) (.f64 (pow.f64 (.f64 -1/2 (log.f64 n)) 2) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (+.f64 (.f64 1/2 (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (PI.f64)))) 2) (.f64 (pow.f64 n 1/2) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (.f64 1/4 (.f64 (pow.f64 n 1/2) (.f64 (pow.f64 (.f64 2 (PI.f64)) 1/2) (.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))) (pow.f64 k 2)) (+.f64 (.f64 (pow.f64 n 1/2) (pow.f64 (.f64 2 (PI.f64)) 1/2)) (.f64 k (+.f64 (.f64 -1/2 (.f64 (pow.f64 n 1/2) (.f64 (log.f64 n) (pow.f64 (.f64 2 (PI.f64)) 1/2)))) (.f64 -1/2 (.f64 (pow.f64 n 1/2) (.f64 (log.f64 (.f64 2 (PI.f64))) (pow.f64 (.f64 2 (PI.f64)) 1/2))))))))
(fma.f64 (fma.f64 1/2 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (.f64 -1/2 (log.f64 n)) 2))) (fma.f64 1/2 (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (PI.f64)))) 2) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 n))) (.f64 (.f64 1/4 (sqrt.f64 n)) (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (log.f64 (.f64 2 (PI.f64)))) (log.f64 n))))) (.f64 k k) (fma.f64 (sqrt.f64 n) (sqrt.f64 (.f64 2 (PI.f64))) (.f64 k (.f64 -1/2 (+.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (log.f64 n))) (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (log.f64 (.f64 2 (PI.f64)))) (sqrt.f64 n)))))))
(fma.f64 (.f64 k k) (fma.f64 1/2 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 (sqrt.f64 n) (pow.f64 (.f64 -1/2 (log.f64 n)) 2))) (fma.f64 1/2 (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (PI.f64)))) 2) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 n))) (.f64 (sqrt.f64 n) (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) 1/4)))) (fma.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 n) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (+.f64 (.f64 (sqrt.f64 n) (log.f64 n)) (.f64 (log.f64 (.f64 2 (PI.f64))) (sqrt.f64 n)))) k))))
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(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))
(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))
(.f64 (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))

localize42.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.2b	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.3b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
✓	3.0b	(expm1.f64 (log1p.f64 (pow.f64 k -1/2)))

Compiler

Compiled 64 to 47 computations (26.6% saved)

series753.0ms (0.9%)

Counts

2 → 24

Calls

9 calls:

Time	Variable		Point	Expression
286.0ms	k	@	-inf	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
247.0ms	n	@	-inf	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
160.0ms	k	@	-inf	(expm1.f64 (log1p.f64 (pow.f64 k -1/2)))
26.0ms	n	@	inf	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
12.0ms	n	@	0	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Compiler

Compiled 73244 to 65976 computations (9.9% saved)

rewrite58.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

761×	`log-prod_binary64`
407×	`pow2_binary64`
279×	`pow1/3_binary64`
276×	`expm1-udef_binary64`
275×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	27
1	328	27
2	4000	26

Stop Event

1×	node limit

Counts

2 → 52

Calls

Call 1

Inputs
(expm1.f64 (log1p.f64 (pow.f64 k -1/2)))
(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (pow.f64 k -1/2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (pow.f64 k -1/2) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 k -1)) (cbrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/4) (pow.f64 k -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 -1/2) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 k) 2) -1/2) (pow.f64 (cbrt.f64 k) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.f64 k) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 (pow.f64 k -1/2) 1) 3) 1) (+.f64 (pow.f64 (+.f64 (pow.f64 k -1/2) 1) 2) (+.f64 1 (*.f64 (+.f64 (pow.f64 k -1/2) 1) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 (pow.f64 k -1/2) 1) 2) 1) (+.f64 (+.f64 (pow.f64 k -1/2) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 k -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 k -1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 k k) -1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 k -1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 k -1))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 -1/2 (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/2 (log.f64 k)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (pow.f64 k -1/2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 k -1/2) 1)) 2) (cbrt.f64 (+.f64 (pow.f64 k -1/2) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (pow.f64 k -1/4)) (hypot.f64 1 (pow.f64 k -1/4)) -1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 4)) (pow.f64 k -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 -1/2 (log.f64 k) (log.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 -1/2 (log.f64 k) (log.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))))) 1))))))

simplify62.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

608×	`times-frac_binary64`
264×	`fma-neg_binary64`
254×	`sqr-pow_binary64`
217×	`div-sub_binary64`
189×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	182	1486
1	464	1444
2	1967	1186
3	3795	1072

Stop Event

1×	node limit

Counts

76 → 84

Calls

Call 1

Inputs
(pow.f64 k -1/2)
(pow.f64 k -1/2)
(pow.f64 k -1/2)
(pow.f64 k -1/2)
(pow.f64 (/.f64 1 k) 1/2)
(pow.f64 (/.f64 1 k) 1/2)
(pow.f64 (/.f64 1 k) 1/2)
(pow.f64 (/.f64 1 k) 1/2)
(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/2) (pow.f64 k -1/2))
(+.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (pow.f64 k -1/2)) (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(+.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (pow.f64 k -1/2)) (+.f64 (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 1/2 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))))))
(+.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (pow.f64 k -1/2)) (+.f64 (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2))))) (.f64 1/6 (.f64 (pow.f64 k -1/2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k 3) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64))))) 3))))))))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) (pow.f64 (/.f64 1 k) 1/2))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) (pow.f64 (/.f64 1 k) 1/2))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) (pow.f64 (/.f64 1 k) 1/2))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) (pow.f64 (/.f64 1 k) 1/2))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (pow.f64 k -1/2))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (pow.f64 k -1/2))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (pow.f64 k -1/2))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (pow.f64 k -1/2))
(.f64 (pow.f64 k -1/2) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (pow.f64 k -1/2) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (pow.f64 k -1/2) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (pow.f64 k -1/2) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(+.f64 (+.f64 (pow.f64 k -1/2) 1) -1)
(+.f64 0 (pow.f64 k -1/2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))))
(-.f64 (+.f64 (pow.f64 k -1/2) 1) 1)
(*.f64 (pow.f64 k -1/2) 1)
(*.f64 1 (pow.f64 k -1/2))
(*.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (pow.f64 k -1)))
(*.f64 (cbrt.f64 (pow.f64 k -1)) (cbrt.f64 (pow.f64 k -1/2)))
(*.f64 (pow.f64 k -1/4) (pow.f64 k -1/4))
(*.f64 (pow.f64 1 -1/2) (pow.f64 k -1/2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 k) 2) -1/2) (pow.f64 (cbrt.f64 k) -1/2))
(*.f64 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.f64 k) -1/2))
(/.f64 (-.f64 (pow.f64 (+.f64 (pow.f64 k -1/2) 1) 3) 1) (+.f64 (pow.f64 (+.f64 (pow.f64 k -1/2) 1) 2) (+.f64 1 (*.f64 (+.f64 (pow.f64 k -1/2) 1) 1))))
(/.f64 (-.f64 (pow.f64 (+.f64 (pow.f64 k -1/2) 1) 2) 1) (+.f64 (+.f64 (pow.f64 k -1/2) 1) 1))
(pow.f64 k -1/2)
(pow.f64 (pow.f64 k -1/2) 1)
(pow.f64 (pow.f64 (pow.f64 k -1/2) 3) 1/3)
(pow.f64 (*.f64 k k) -1/4)
(pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3)
(pow.f64 (pow.f64 k -1/4) 2)
(pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2)
(sqrt.f64 (pow.f64 k -1))
(log.f64 (exp.f64 (pow.f64 k -1/2)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 k -1/2))))
(cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3))
(log1p.f64 (expm1.f64 (pow.f64 k -1/2)))
(exp.f64 (*.f64 -1/2 (log.f64 k)))
(exp.f64 (.f64 (.f64 -1/2 (log.f64 k)) 1))
(fma.f64 1 (+.f64 (pow.f64 k -1/2) 1) -1)
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 k -1/2) 1)) 2) (cbrt.f64 (+.f64 (pow.f64 k -1/2) 1)) -1)
(fma.f64 (hypot.f64 1 (pow.f64 k -1/4)) (hypot.f64 1 (pow.f64 k -1/4)) -1)
(+.f64 0 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (-.f64 1 k))))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (-.f64 1 k)))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (-.f64 1 k)))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (-.f64 1 k)))))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))))) 1)
(pow.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))) 1)
(pow.f64 (pow.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))) 3) 1/3)
(pow.f64 (cbrt.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))))) 3)
(pow.f64 (.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 4)) (pow.f64 k -1/4)) 2)
(pow.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))) 3)) 1/3)
(pow.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)
(sqrt.f64 (.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)) (pow.f64 k -1)))
(log.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (-.f64 1 k)))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))))))
(cbrt.f64 (pow.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))) 3))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))) 3)))
(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(expm1.f64 (log1p.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))))))
(log1p.f64 (expm1.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))))))
(exp.f64 (fma.f64 -1/2 (log.f64 k) (log.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (-.f64 1 k))))))
(exp.f64 (.f64 (fma.f64 -1/2 (log.f64 k) (log.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))))) 1))

Outputs
(pow.f64 k -1/2)
(pow.f64 k -1/2)
(pow.f64 k -1/2)
(pow.f64 k -1/2)
(pow.f64 (/.f64 1 k) 1/2)
(pow.f64 k -1/2)
(pow.f64 (/.f64 1 k) 1/2)
(pow.f64 k -1/2)
(pow.f64 (/.f64 1 k) 1/2)
(pow.f64 k -1/2)
(pow.f64 (/.f64 1 k) 1/2)
(pow.f64 k -1/2)
(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/2) (pow.f64 k -1/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(+.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (pow.f64 k -1/2)) (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(fma.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))))
(fma.f64 -1/2 (.f64 k (.f64 (pow.f64 k -1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (+.f64 (pow.f64 k -1/2) (.f64 (.f64 k -1/2) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))))
(+.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (pow.f64 k -1/2)) (+.f64 (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 1/2 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))))))
(fma.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2) (fma.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 1/2 (.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2))) (*.f64 k k)))))
(fma.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (fma.f64 -1/2 (.f64 k (.f64 (pow.f64 k -1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 (.f64 (pow.f64 k -1/2) (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 1/2 (*.f64 k k)))))
(fma.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (+.f64 (.f64 (.f64 k -1/2) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 (.f64 1/2 (.f64 k k)) (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64))))) 2))))))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (+.f64 (pow.f64 k -1/2) (+.f64 (.f64 (.f64 k -1/2) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 (.f64 1/2 (.f64 k k)) (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64))))) 2))))))
(+.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (pow.f64 k -1/2)) (+.f64 (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2))))) (.f64 1/6 (.f64 (pow.f64 k -1/2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k 3) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64))))) 3))))))))
(fma.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2) (fma.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (fma.f64 1/2 (.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2))) (.f64 k k)) (.f64 1/6 (.f64 (pow.f64 k -1/2) (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (pow.f64 k 3) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64))))) 3))))))))
(fma.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (fma.f64 -1/2 (.f64 k (.f64 (pow.f64 k -1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))) (fma.f64 1/6 (.f64 (pow.f64 k -1/2) (.f64 (.f64 -1/8 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k 3)))) (.f64 (.f64 (pow.f64 k -1/2) (.f64 (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 1/2 (*.f64 k k))))))
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(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (+.f64 (+.f64 (pow.f64 k -1/2) (.f64 (.f64 k -1/2) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (.f64 (.f64 1/2 (.f64 k k)) (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2))) (.f64 (.f64 (pow.f64 k -1/2) 1/6) (.f64 -1/8 (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 3) (pow.f64 k 3)))))))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) (pow.f64 (/.f64 1 k) 1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) (pow.f64 (/.f64 1 k) 1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) (pow.f64 (/.f64 1 k) 1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) (pow.f64 (/.f64 1 k) 1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (pow.f64 k -1/2) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (pow.f64 k -1/2) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (pow.f64 k -1/2) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
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(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (pow.f64 k -1/2) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(+.f64 (+.f64 (pow.f64 k -1/2) 1) -1)
(pow.f64 k -1/2)
(+.f64 0 (pow.f64 k -1/2))
(pow.f64 k -1/2)
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2)))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))))
(pow.f64 k -1/2)
(-.f64 (+.f64 (pow.f64 k -1/2) 1) 1)
(pow.f64 k -1/2)
(*.f64 (pow.f64 k -1/2) 1)
(pow.f64 k -1/2)
(*.f64 1 (pow.f64 k -1/2))
(pow.f64 k -1/2)
(*.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (pow.f64 k -1)))
(pow.f64 k -1/2)
(*.f64 (cbrt.f64 (pow.f64 k -1)) (cbrt.f64 (pow.f64 k -1/2)))
(pow.f64 k -1/2)
(*.f64 (pow.f64 k -1/4) (pow.f64 k -1/4))
(pow.f64 k -1/2)
(*.f64 (pow.f64 1 -1/2) (pow.f64 k -1/2))
(pow.f64 k -1/2)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 k) 2) -1/2) (pow.f64 (cbrt.f64 k) -1/2))
(*.f64 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.f64 k) -1/2))
(pow.f64 (sqrt.f64 k) -1)
(/.f64 1 (sqrt.f64 k))
(/.f64 (-.f64 (pow.f64 (+.f64 (pow.f64 k -1/2) 1) 3) 1) (+.f64 (pow.f64 (+.f64 (pow.f64 k -1/2) 1) 2) (+.f64 1 (*.f64 (+.f64 (pow.f64 k -1/2) 1) 1))))
(/.f64 (+.f64 (pow.f64 (+.f64 (pow.f64 k -1/2) 1) 3) -1) (+.f64 (pow.f64 (+.f64 (pow.f64 k -1/2) 1) 2) (+.f64 (pow.f64 k -1/2) 2)))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (pow.f64 k -1/2) 1) 3)) (+.f64 (pow.f64 k -1/2) (+.f64 2 (pow.f64 (+.f64 (pow.f64 k -1/2) 1) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (pow.f64 k -1/2) 1) 3)) (fma.f64 (+.f64 (pow.f64 k -1/2) 1) (+.f64 (pow.f64 k -1/2) 2) 1))
(/.f64 (-.f64 (pow.f64 (+.f64 (pow.f64 k -1/2) 1) 2) 1) (+.f64 (+.f64 (pow.f64 k -1/2) 1) 1))
(pow.f64 k -1/2)
(pow.f64 k -1/2)
(pow.f64 (pow.f64 k -1/2) 1)
(pow.f64 k -1/2)
(pow.f64 (pow.f64 (pow.f64 k -1/2) 3) 1/3)
(pow.f64 k -1/2)
(pow.f64 (*.f64 k k) -1/4)
(pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3)
(pow.f64 k -1/2)
(pow.f64 (pow.f64 k -1/4) 2)
(pow.f64 k -1/2)
(pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2)
(pow.f64 (sqrt.f64 k) -1)
(/.f64 1 (sqrt.f64 k))
(sqrt.f64 (pow.f64 k -1))
(pow.f64 k -1/2)
(log.f64 (exp.f64 (pow.f64 k -1/2)))
(pow.f64 k -1/2)
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 k -1/2))))
(pow.f64 k -1/2)
(cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3))
(pow.f64 k -1/2)
(log1p.f64 (expm1.f64 (pow.f64 k -1/2)))
(pow.f64 k -1/2)
(exp.f64 (*.f64 -1/2 (log.f64 k)))
(pow.f64 k -1/2)
(exp.f64 (.f64 (.f64 -1/2 (log.f64 k)) 1))
(pow.f64 k -1/2)
(fma.f64 1 (+.f64 (pow.f64 k -1/2) 1) -1)
(pow.f64 k -1/2)
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 k -1/2) 1)) 2) (cbrt.f64 (+.f64 (pow.f64 k -1/2) 1)) -1)
(pow.f64 k -1/2)
(fma.f64 (hypot.f64 1 (pow.f64 k -1/4)) (hypot.f64 1 (pow.f64 k -1/4)) -1)
(pow.f64 k -1/2)
(+.f64 0 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (-.f64 1 k))))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (-.f64 1 k)))))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))))
(.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (-.f64 1 k)))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (-.f64 1 k)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(-.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))))) 1)
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))) 1)
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (pow.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))) 3) 1/3)
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (cbrt.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))))) 3)
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 4)) (pow.f64 k -1/4)) 2)
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))) 3)) 1/3)
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)) (pow.f64 k -1)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(log.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(cbrt.f64 (pow.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k)))) 3))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))) 3)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(expm1.f64 (log1p.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(log1p.f64 (expm1.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(exp.f64 (fma.f64 -1/2 (log.f64 k) (log.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (-.f64 1 k))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(exp.f64 (.f64 (fma.f64 -1/2 (log.f64 k) (log.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))))) 1))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (.f64 1/2 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (fabs.f64 (pow.f64 k -1/2)) (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))

eval450.0ms (0.5%)

Compiler: Compiled 22902 to 15757 computations (31.2% saved)

prune269.0ms (0.3%)

Pruning

39 alts after pruning (35 fresh and 4 done)

	Pruned	Kept	Total
New	975	27	1002
Fresh	12	8	20
Picked	0	1	1
Done	2	3	5
Total	989	39	1028

Error

Counts

1028 → 39

Alt Table

Click to see full alt table

Status	Error	Program
	40.1b	(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2) 1/3)
	32.9b	(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/4) 2)
	35.2b	(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/6) 3)
	10.5b	(pow.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))) -1/2)
	11.1b	(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))) 3)
✓	0.4b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	3.5b	(/.f64 (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
	22.9b	(/.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 3/2) (sqrt.f64 k))
	0.4b	(/.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) -1/2))
✓	0.3b	(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 n 2) (PI.f64))) (pow.f64 (.f64 (.f64 n 2) (PI.f64)) (.f64 k -1/2))) (sqrt.f64 k))
✓	22.6b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
	3.4b	(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
	34.3b	(/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3/2)) (sqrt.f64 k))
	10.6b	(/.f64 1 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))))) 2))
▶	0.3b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n 2) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k) (PI.f64))))))
	22.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
	10.6b	(/.f64 1 (/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))))
	32.7b	(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 2 n))))
	32.7b	(/.f64 1 (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 2 n)))))
▶	0.5b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	0.5b	(.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) -1/2)))
	22.7b	(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))))
	0.4b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k 1/4)))
	3.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
	22.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
	3.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
	0.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.3b	(.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 k -1/2)) (pow.f64 k -1/2)))
	22.8b	(.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 k)))
✓	3.2b	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.2b	(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	10.6b	(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))
	32.7b	(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
	32.8b	(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
	33.0b	(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
▶	33.0b	(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
▶	34.7b	(exp.f64 (.f64 (log.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))) 1/2))
	12.5b	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))
	38.4b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2))

Compiler

Compiled 1145 to 942 computations (17.7% saved)

localize42.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n 2) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k) (PI.f64))))))
✓	0.2b	(/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n 2) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k) (PI.f64)))))
✓	0.2b	(/.f64 (.f64 n 2) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k) (PI.f64)))
	0.2b	(.f64 n (.f64 2 (PI.f64)))

Compiler

Compiled 99 to 61 computations (38.4% saved)

series13.4s (15.8%)

Counts

3 → 20

Calls

18 calls:

Time	Variable		Point	Expression
1.9s	n	@	inf	(/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n 2) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k) (PI.f64)))))
1.6s	n	@	-inf	(/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n 2) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k) (PI.f64)))))
1.5s	k	@	0	(/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n 2) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k) (PI.f64)))))
1.5s	n	@	0	(/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n 2) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k) (PI.f64)))))
1.3s	k	@	0	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n 2) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k) (PI.f64))))))

Compiler

Compiled 1690895 to 1164928 computations (31.1% saved)

rewrite83.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

436×	`pow2_binary64`
304×	`pow1/3_binary64`
295×	`expm1-udef_binary64`
295×	`log1p-udef_binary64`
280×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	76
1	351	73
2	4941	73

Stop Event

1×	node limit

Counts

3 → 142

Calls

Call 1

Inputs

(/.f64 (*.f64 n 2) (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k) (PI.f64)))

(/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k) (PI.f64)))))

(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k) (PI.f64))))))

Outputs

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k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))) (sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 2 (*.f64 n (/.f64 (PI.f64) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))))) (sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 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simplify100.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

512×	`distribute-rgt-in_binary64`
422×	`log-prod_binary64`
389×	`fma-def_binary64`
256×	`associate-r_binary64`
238×	`cube-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	382	5394
1	1005	5128
2	3875	4812

Stop Event

1×	node limit

Counts

162 → 255

Calls

Call 1

Inputs
(.f64 2 (/.f64 (.f64 n (PI.f64)) (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(.f64 2 (/.f64 (.f64 n (PI.f64)) (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(.f64 2 (/.f64 (.f64 n (PI.f64)) (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(.f64 2 (/.f64 (.f64 n (PI.f64)) (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(.f64 2 (/.f64 (.f64 n (PI.f64)) (exp.f64 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 2 (/.f64 (.f64 n (PI.f64)) (exp.f64 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 2 (/.f64 (.f64 n (PI.f64)) (exp.f64 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 2 (/.f64 (.f64 n (PI.f64)) (exp.f64 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 2 (.f64 n (PI.f64)))
(+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 -2 (.f64 k (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64))))))
(+.f64 (.f64 -2 (.f64 (pow.f64 k 2) (+.f64 (.f64 1/2 (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (PI.f64)))) (.f64 -1 (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (PI.f64))))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 -2 (.f64 k (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64)))))))
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(.f64 2 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))
(-.f64 (exp.f64 (log1p.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))))) 1)
(.f64 n (/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (PI.f64)))))
(.f64 n (.f64 2 (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k))))
(.f64 2 (/.f64 n (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) (PI.f64))))
(.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k))))
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(.f64 (PI.f64) (/.f64 (.f64 n 2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))
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(.f64 1 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k)))))
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(.f64 (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)) (.f64 n 2))
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(.f64 (/.f64 2 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k)) (/.f64 n (/.f64 1 (PI.f64))))
(.f64 (/.f64 n (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k)) (/.f64 2 (/.f64 1 (PI.f64))))
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(.f64 (/.f64 2 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (PI.f64))) 2)) (/.f64 n (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) (PI.f64)))))
(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (PI.f64))) 2)) (/.f64 (.f64 n 2) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (PI.f64)))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 n 2)) 2) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (PI.f64))) 2)) (cbrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k))))))
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(.f64 (/.f64 2 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (PI.f64)))) (/.f64 n (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) (PI.f64)))))
(.f64 (/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (PI.f64)))) (/.f64 (.f64 n 2) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (PI.f64)))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 n 2)) 2) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (PI.f64)))) (/.f64 (cbrt.f64 (.f64 n 2)) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) (PI.f64)))))
(.f64 (/.f64 (.f64 n 2) 1) (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))
(.f64 (/.f64 (.f64 n 2) (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k))) (neg.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k))))) (cbrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))))))
(.f64 (.f64 (/.f64 (.f64 n 2) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k)) 1) (PI.f64))
(.f64 (.f64 (/.f64 (.f64 n 2) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k)) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (/.f64 (.f64 n 2) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(pow.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) 1)
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k))))) 2)
(pow.f64 (pow.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) 2) 1/2)
(pow.f64 (pow.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) 3) 1/3)
(pow.f64 (cbrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k))))) 3)
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (.f64 (PI.f64) n))) -1)
(pow.f64 (/.f64 (pow.f64 (.f64 n 2) 3) (pow.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) (PI.f64)) 3)) 1/3)
(pow.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (.f64 (PI.f64) n))) 1) -1)
(neg.f64 (/.f64 (.f64 n 2) (/.f64 (neg.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k)) (PI.f64))))
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(log.f64 (+.f64 1 (expm1.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))))))
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(.f64 (sqrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (.f64 (PI.f64) n))))) 1)
(.f64 1 (sqrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (.f64 (PI.f64) n))))))
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(neg.f64 (/.f64 (sqrt.f64 k) (neg.f64 (sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k))))))))
(sqrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (*.f64 (PI.f64) n)))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (*.f64 (PI.f64) n)))))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (*.f64 (PI.f64) n))))))))
(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (*.f64 (PI.f64) n))))) 3))
(cbrt.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) 3/2)))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (*.f64 (PI.f64) n)))))))
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(exp.f64 (log.f64 (sqrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (*.f64 (PI.f64) n)))))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (.f64 (PI.f64) n)))))) 1))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k)))) 1)
(.f64 (sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k))))) (pow.f64 k -1/2))
(.f64 1 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k)))) k)))
(.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k)))) k)) 1)
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k))) (cbrt.f64 (/.f64 1 (.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (.f64 (PI.f64) n)))))))
(.f64 (cbrt.f64 (/.f64 1 (.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (.f64 (PI.f64) n)))))) (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k))))
(.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k))) (sqrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k)))) k))))
(.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (.f64 (PI.f64) n))))))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k))))))
(.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k)))) -1/2)))
(.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k))))) 1) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k)))))) (sqrt.f64 k)))
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(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k))))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k))))) (cbrt.f64 k)) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k)))))) (cbrt.f64 (sqrt.f64 k))))
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(.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k))))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k)))))) (pow.f64 k 1/4)))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) 1/4) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k)))) 1/4) (pow.f64 k 1/4)))
(.f64 (/.f64 1 (neg.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k)))))))
(.f64 (/.f64 1 (cbrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (.f64 (PI.f64) n)))))) (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k))))
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(.f64 (.f64 (pow.f64 k -1/2) (cbrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))))))
(.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) 1/4)) (pow.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) 1/4))
(pow.f64 (sqrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (*.f64 (PI.f64) n))))) -1)
(pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k)) 1)
(pow.f64 (.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (*.f64 (PI.f64) n)))) -1/2)
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k)) 3) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k))) 3)
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(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) 3/2) (pow.f64 k 3/2)) 1/3)
(pow.f64 (neg.f64 (neg.f64 (sqrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (*.f64 (PI.f64) n))))))) -1)
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(sqrt.f64 (/.f64 1 (.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (*.f64 (PI.f64) n))))))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) 3/2) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k))))
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Outputs
(.f64 2 (/.f64 (.f64 n (PI.f64)) (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 (.f64 (.f64 2 n) (PI.f64)) (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(.f64 2 (.f64 (/.f64 n (pow.f64 (exp.f64 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (PI.f64)))
(.f64 2 (/.f64 (PI.f64) (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 (.f64 (.f64 2 n) (PI.f64)) (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(.f64 2 (.f64 (/.f64 n (pow.f64 (exp.f64 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (PI.f64)))
(.f64 2 (/.f64 (PI.f64) (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 (.f64 (.f64 2 n) (PI.f64)) (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(.f64 2 (.f64 (/.f64 n (pow.f64 (exp.f64 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (PI.f64)))
(.f64 2 (/.f64 (PI.f64) (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 (.f64 (.f64 2 n) (PI.f64)) (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(.f64 2 (.f64 (/.f64 n (pow.f64 (exp.f64 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (PI.f64)))
(.f64 2 (/.f64 (PI.f64) (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) (exp.f64 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 (.f64 (.f64 2 n) (PI.f64)) (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(.f64 2 (.f64 (/.f64 n (pow.f64 (exp.f64 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (PI.f64)))
(.f64 2 (/.f64 (PI.f64) (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) (exp.f64 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 (.f64 (.f64 2 n) (PI.f64)) (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
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(/.f64 1 (sqrt.f64 (.f64 (/.f64 k 2) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k) (.f64 n (PI.f64))))))
(/.f64 1 (sqrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k) (.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) 1/4) (pow.f64 k 1/4)) 2)
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) k)))) (pow.f64 k 1/4)))
(/.f64 1 (/.f64 (pow.f64 k 1/2) (sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k) n)))) (/.f64 1 (sqrt.f64 k)))
(sqrt.f64 (/.f64 1 (.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (*.f64 (PI.f64) n))))))
(sqrt.f64 (/.f64 2 (/.f64 k (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) k)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(sqrt.f64 (.f64 (/.f64 2 k) (/.f64 (PI.f64) (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) n))))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k))
(sqrt.f64 (/.f64 2 (/.f64 k (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) k)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(sqrt.f64 (.f64 (/.f64 2 k) (/.f64 (PI.f64) (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) n))))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k))))
(sqrt.f64 (/.f64 2 (/.f64 k (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) k)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(sqrt.f64 (.f64 (/.f64 2 k) (/.f64 (PI.f64) (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) n))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k)))))
(sqrt.f64 (/.f64 2 (/.f64 k (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) k)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(sqrt.f64 (.f64 (/.f64 2 k) (/.f64 (PI.f64) (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) n))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k)) 3))
(sqrt.f64 (/.f64 2 (/.f64 k (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) k)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(sqrt.f64 (.f64 (/.f64 2 k) (/.f64 (PI.f64) (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) n))))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) 3/2) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 (.f64 2 n) (PI.f64)) k))) 3/2) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))) 3/2) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) n))) 3/2) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k))))
(sqrt.f64 (/.f64 2 (/.f64 k (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) k)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(sqrt.f64 (.f64 (/.f64 2 k) (/.f64 (PI.f64) (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) n))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k))))
(sqrt.f64 (/.f64 2 (/.f64 k (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) k)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(sqrt.f64 (.f64 (/.f64 2 k) (/.f64 (PI.f64) (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) n))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k))))
(sqrt.f64 (/.f64 2 (/.f64 k (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) k)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(sqrt.f64 (.f64 (/.f64 2 k) (/.f64 (PI.f64) (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) n))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (.f64 (PI.f64) n)))))) -1))
(/.f64 -1 (neg.f64 (sqrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) k) (.f64 (*.f64 2 n) (PI.f64)))))))
(/.f64 1 (sqrt.f64 (.f64 (/.f64 k 2) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k) (.f64 n (PI.f64))))))
(/.f64 1 (sqrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k) (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k)))) k))) 1))
(sqrt.f64 (/.f64 2 (/.f64 k (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) k)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(sqrt.f64 (.f64 (/.f64 2 k) (/.f64 (PI.f64) (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) n))))

localize12.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (/.f64 2 k) (PI.f64))
✓	0.5b	(.f64 n (.f64 (/.f64 2 k) (PI.f64)))
✓	9.8b	(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))

Compiler

Compiled 29 to 18 computations (37.9% saved)

series2.3s (2.7%)

Counts

3 → 36

Calls

15 calls:

Time	Variable		Point	Expression
436.0ms	k	@	-inf	(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
385.0ms	k	@	inf	(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
378.0ms	n	@	0	(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
373.0ms	n	@	-inf	(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
357.0ms	n	@	inf	(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))

Compiler

Compiled 260432 to 164116 computations (37% saved)

rewrite62.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

916×	`pow1_binary64`
848×	`add-log-exp_binary64`
848×	`log1p-expm1-u_binary64`
848×	`expm1-log1p-u_binary64`
829×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	32
1	190	32
2	2335	32

Stop Event

1×	node limit

Counts

3 → 63

Calls

Call 1

Inputs
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(.f64 n (.f64 (/.f64 2 k) (PI.f64)))
(*.f64 (/.f64 2 k) (PI.f64))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k)) (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k))) (cbrt.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 2 k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k) 1/4) (pow.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 2 k) (PI.f64))) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k)) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n (/.f64 2 k))) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k)) 2) 1/2) (pow.f64 (cbrt.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n (/.f64 2 k)) 1/2) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (PI.f64)) n) k)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 2 (PI.f64))) k)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 (/.f64 2 k)) (PI.f64)) n))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (*.f64 (/.f64 2 k) (PI.f64)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (/.f64 2 k) (PI.f64)) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (*.f64 (*.f64 2 (PI.f64)) n) k)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (/.f64 2 k) (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 2 (/.f64 k (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (PI.f64) (*.f64 k 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 k (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (PI.f64)) k)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (PI.f64))) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 2 (PI.f64)) 1) k)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 2 (PI.f64)) (cbrt.f64 (*.f64 k k))) (cbrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 2 (PI.f64)) (sqrt.f64 k)) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -2 (PI.f64)) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) -2) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 2 k) (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 2 k) (PI.f64)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 2 k) (PI.f64))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (/.f64 2 k) (PI.f64))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (/.f64 2 k) (PI.f64)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (/.f64 2 k)) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 2 k) (PI.f64)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 2 k) 3) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 2 k) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (/.f64 2 k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (/.f64 2 k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (/.f64 2 k) (PI.f64))))))))

simplify57.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

779×	`log-prod_binary64`
577×	`log-div_binary64`
523×	`unswap-sqr_binary64`
429×	`associate-*l/_binary64`
382×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	144	1218
1	316	1170
2	1187	1124
3	6311	1124

Stop Event

1×	node limit

Counts

99 → 89

Calls

Call 1

Inputs
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (PI.f64) k))
(*.f64 2 (/.f64 (PI.f64) k))
(*.f64 2 (/.f64 (PI.f64) k))
(*.f64 2 (/.f64 (PI.f64) k))
(*.f64 2 (/.f64 (PI.f64) k))
(*.f64 2 (/.f64 (PI.f64) k))
(*.f64 2 (/.f64 (PI.f64) k))
(*.f64 2 (/.f64 (PI.f64) k))
(*.f64 2 (/.f64 (PI.f64) k))
(*.f64 2 (/.f64 (PI.f64) k))
(*.f64 2 (/.f64 (PI.f64) k))
(*.f64 2 (/.f64 (PI.f64) k))
(-.f64 (+.f64 1 (sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k))) 1)
(.f64 (sqrt.f64 (/.f64 (.f64 (*.f64 2 (PI.f64)) n) k)) 1)
(.f64 1 (sqrt.f64 (/.f64 (.f64 (*.f64 2 (PI.f64)) n) k)))
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Outputs
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(+.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2)))) 0)
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(fabs.f64 (sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k)))
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64))))) 1))
(+.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2)))) 0)
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k))))
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64))))) 1))
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(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(cbrt.f64 (pow.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k) 3/2))
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(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))) 3/2))
(cbrt.f64 (pow.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k))))
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64))))) 1))
(+.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2)))) 0)
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k))))
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64))))) 1))
(+.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2)))) 0)
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k))))
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64))))) 1))
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(-.f64 (+.f64 1 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k)) 1)
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 n (/.f64 (PI.f64) (/.f64 k 2)))
(.f64 n (.f64 2 (/.f64 (PI.f64) k)))
(/.f64 (.f64 (.f64 2 (PI.f64)) n) k)
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 n (/.f64 (PI.f64) (/.f64 k 2)))
(.f64 n (.f64 2 (/.f64 (PI.f64) k)))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 n (/.f64 (PI.f64) (/.f64 k 2)))
(.f64 n (.f64 2 (/.f64 (PI.f64) k)))
(pow.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k) 1)
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 n (/.f64 (PI.f64) (/.f64 k 2)))
(.f64 n (.f64 2 (/.f64 (PI.f64) k)))
(pow.f64 (sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k)) 2)
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 n (/.f64 (PI.f64) (/.f64 k 2)))
(.f64 n (.f64 2 (/.f64 (PI.f64) k)))
(pow.f64 (pow.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k) 2) 1/2)
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 n (/.f64 (PI.f64) (/.f64 k 2)))
(.f64 n (.f64 2 (/.f64 (PI.f64) k)))
(pow.f64 (pow.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k) 3) 1/3)
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 n (/.f64 (PI.f64) (/.f64 k 2)))
(.f64 n (.f64 2 (/.f64 (PI.f64) k)))
(pow.f64 (cbrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k)) 3)
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 n (/.f64 (PI.f64) (/.f64 k 2)))
(.f64 n (.f64 2 (/.f64 (PI.f64) k)))
(sqrt.f64 (pow.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k) 2))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 n (/.f64 (PI.f64) (/.f64 k 2)))
(.f64 n (.f64 2 (/.f64 (PI.f64) k)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (/.f64 2 k)) (PI.f64)) n))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 n (/.f64 (PI.f64) (/.f64 k 2)))
(.f64 n (.f64 2 (/.f64 (PI.f64) k)))
(cbrt.f64 (pow.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k) 3))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 n (/.f64 (PI.f64) (/.f64 k 2)))
(.f64 n (.f64 2 (/.f64 (PI.f64) k)))
(cbrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 (/.f64 2 k) (PI.f64)) 3)))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 n (/.f64 (PI.f64) (/.f64 k 2)))
(.f64 n (.f64 2 (/.f64 (PI.f64) k)))
(cbrt.f64 (.f64 (pow.f64 (.f64 (/.f64 2 k) (PI.f64)) 3) (pow.f64 n 3)))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 n (/.f64 (PI.f64) (/.f64 k 2)))
(.f64 n (.f64 2 (/.f64 (PI.f64) k)))
(expm1.f64 (log1p.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k)))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 n (/.f64 (PI.f64) (/.f64 k 2)))
(.f64 n (.f64 2 (/.f64 (PI.f64) k)))
(log1p.f64 (expm1.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k)))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 n (/.f64 (PI.f64) (/.f64 k 2)))
(.f64 n (.f64 2 (/.f64 (PI.f64) k)))
(exp.f64 (log.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k)))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 n (/.f64 (PI.f64) (/.f64 k 2)))
(.f64 n (.f64 2 (/.f64 (PI.f64) k)))
(-.f64 (+.f64 1 (*.f64 (/.f64 2 k) (PI.f64))) 1)
(*.f64 (PI.f64) (/.f64 2 k))
(/.f64 (PI.f64) (/.f64 k 2))
(*.f64 2 (/.f64 (PI.f64) k))
(/.f64 2 (/.f64 k (PI.f64)))
(*.f64 (PI.f64) (/.f64 2 k))
(/.f64 (PI.f64) (/.f64 k 2))
(*.f64 2 (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (*.f64 k 1/2))
(*.f64 (PI.f64) (/.f64 2 k))
(/.f64 (PI.f64) (/.f64 k 2))
(*.f64 2 (/.f64 (PI.f64) k))
(/.f64 1 (/.f64 k (*.f64 2 (PI.f64))))
(*.f64 (PI.f64) (/.f64 2 k))
(/.f64 (PI.f64) (/.f64 k 2))
(*.f64 2 (/.f64 (PI.f64) k))
(/.f64 (*.f64 2 (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 2 k))
(/.f64 (PI.f64) (/.f64 k 2))
(*.f64 2 (/.f64 (PI.f64) k))
(/.f64 (neg.f64 (*.f64 2 (PI.f64))) (neg.f64 k))
(*.f64 (PI.f64) (/.f64 2 k))
(/.f64 (PI.f64) (/.f64 k 2))
(*.f64 2 (/.f64 (PI.f64) k))
(/.f64 (/.f64 (*.f64 2 (PI.f64)) 1) k)
(*.f64 (PI.f64) (/.f64 2 k))
(/.f64 (PI.f64) (/.f64 k 2))
(*.f64 2 (/.f64 (PI.f64) k))
(/.f64 (/.f64 (.f64 2 (PI.f64)) (cbrt.f64 (.f64 k k))) (cbrt.f64 k))
(.f64 (/.f64 2 (cbrt.f64 k)) (/.f64 (PI.f64) (cbrt.f64 (.f64 k k))))
(/.f64 (/.f64 (*.f64 2 (PI.f64)) (sqrt.f64 k)) (sqrt.f64 k))
(*.f64 (PI.f64) (/.f64 2 k))
(/.f64 (PI.f64) (/.f64 k 2))
(*.f64 2 (/.f64 (PI.f64) k))
(/.f64 (*.f64 -2 (PI.f64)) (neg.f64 k))
(*.f64 (PI.f64) (/.f64 2 k))
(/.f64 (PI.f64) (/.f64 k 2))
(*.f64 2 (/.f64 (PI.f64) k))
(/.f64 (*.f64 (PI.f64) -2) (neg.f64 k))
(*.f64 (PI.f64) (/.f64 2 k))
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(*.f64 2 (/.f64 (PI.f64) k))
(pow.f64 (*.f64 (/.f64 2 k) (PI.f64)) 1)
(*.f64 (PI.f64) (/.f64 2 k))
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(pow.f64 (pow.f64 (*.f64 (/.f64 2 k) (PI.f64)) 3) 1/3)
(*.f64 (PI.f64) (/.f64 2 k))
(/.f64 (PI.f64) (/.f64 k 2))
(*.f64 2 (/.f64 (PI.f64) k))
(pow.f64 (cbrt.f64 (*.f64 (/.f64 2 k) (PI.f64))) 3)
(*.f64 (PI.f64) (/.f64 2 k))
(/.f64 (PI.f64) (/.f64 k 2))
(*.f64 2 (/.f64 (PI.f64) k))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 2 k) (PI.f64))) 2)
(*.f64 (PI.f64) (/.f64 2 k))
(/.f64 (PI.f64) (/.f64 k 2))
(*.f64 2 (/.f64 (PI.f64) k))
(sqrt.f64 (pow.f64 (*.f64 (/.f64 2 k) (PI.f64)) 2))
(*.f64 (PI.f64) (/.f64 2 k))
(/.f64 (PI.f64) (/.f64 k 2))
(*.f64 2 (/.f64 (PI.f64) k))
(log.f64 (pow.f64 (exp.f64 (/.f64 2 k)) (PI.f64)))
(*.f64 (PI.f64) (/.f64 2 k))
(/.f64 (PI.f64) (/.f64 k 2))
(*.f64 2 (/.f64 (PI.f64) k))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 2 k) (PI.f64)) 3))
(*.f64 (PI.f64) (/.f64 2 k))
(/.f64 (PI.f64) (/.f64 k 2))
(*.f64 2 (/.f64 (PI.f64) k))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 2 k) 3) (pow.f64 (PI.f64) 3)))
(*.f64 (PI.f64) (/.f64 2 k))
(/.f64 (PI.f64) (/.f64 k 2))
(*.f64 2 (/.f64 (PI.f64) k))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 2 k) 3)))
(*.f64 (PI.f64) (/.f64 2 k))
(/.f64 (PI.f64) (/.f64 k 2))
(*.f64 2 (/.f64 (PI.f64) k))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 2 k) (PI.f64))))
(*.f64 (PI.f64) (/.f64 2 k))
(/.f64 (PI.f64) (/.f64 k 2))
(*.f64 2 (/.f64 (PI.f64) k))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 2 k) (PI.f64))))
(*.f64 (PI.f64) (/.f64 2 k))
(/.f64 (PI.f64) (/.f64 k 2))
(*.f64 2 (/.f64 (PI.f64) k))
(exp.f64 (log.f64 (*.f64 (/.f64 2 k) (PI.f64))))
(*.f64 (PI.f64) (/.f64 2 k))
(/.f64 (PI.f64) (/.f64 k 2))
(*.f64 2 (/.f64 (PI.f64) k))

localize22.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
✓	4.6b	(exp.f64 (.f64 (log.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))) 1/2))
✓	9.9b	(log.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))

Compiler

Compiled 49 to 28 computations (42.9% saved)

series2.6s (3.1%)

Counts

3 → 40

Calls

18 calls:

Time	Variable		Point	Expression
429.0ms	k	@	-inf	(exp.f64 (.f64 (log.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))) 1/2))
395.0ms	n	@	-inf	(exp.f64 (.f64 (log.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))) 1/2))
383.0ms	k	@	inf	(exp.f64 (.f64 (log.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))) 1/2))
362.0ms	n	@	0	(exp.f64 (.f64 (log.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))) 1/2))
352.0ms	n	@	inf	(exp.f64 (.f64 (log.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))) 1/2))

Compiler

Compiled 291280 to 190848 computations (34.5% saved)

rewrite82.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

672×	`log-prod_binary64`
335×	`pow-prod-down_binary64`
311×	`pow2_binary64`
231×	`pow-unpow_binary64`
218×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	38
1	250	37
2	3322	37

Stop Event

1×	node limit

Counts

3 → 283

Calls

Call 1

Inputs
(log.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))) 1/2))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))

Outputs

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simplify131.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

475×	`log-prod_binary64`
381×	`fma-neg_binary64`
310×	`sqr-pow_binary64`
269×	`log-div_binary64`
230×	`div-sub_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	672	6782
1	1623	6477
2	5029	6367

Stop Event

1×	node limit

Counts

323 → 446

Calls

Call 1

Inputs
(+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))
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Outputs
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(pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 2))) (cbrt.f64 (cbrt.f64 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))))
(pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)))) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)))) 2))) (cbrt.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n))))))
(pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k))))) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k))))) 2))) (cbrt.f64 (cbrt.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k)))))))
(pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 2)) (sqrt.f64 (cbrt.f64 (log.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))) (sqrt.f64 (cbrt.f64 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))))
(pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)))) 2)) (sqrt.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)))))) (sqrt.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n))))))
(pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k))))) 2)) (sqrt.f64 (cbrt.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k))))))) (sqrt.f64 (cbrt.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k)))))))
(pow.f64 (pow.f64 (exp.f64 1) (cbrt.f64 (log.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))) (pow.f64 (cbrt.f64 (log.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 2))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(.f64 n (.f64 (PI.f64) (/.f64 2 k)))
(pow.f64 (pow.f64 (exp.f64 1) (pow.f64 (cbrt.f64 (log.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 2)) (cbrt.f64 (log.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(.f64 n (.f64 (PI.f64) (/.f64 2 k)))
(pow.f64 (pow.f64 (exp.f64 1) (sqrt.f64 (log.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))) (sqrt.f64 (log.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(.f64 n (.f64 (PI.f64) (/.f64 2 k)))
(pow.f64 (.f64 (exp.f64 1) (exp.f64 1)) (log.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(.f64 n (.f64 (PI.f64) (/.f64 2 k)))
(pow.f64 (.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))) (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))))
(pow.f64 (exp.f64 (.f64 2 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n))))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 (/.f64 2 k) n))))))
(pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k))))))) 2) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k)))))))
(pow.f64 (.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))) 2)) (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))) 2))) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))))
(pow.f64 (exp.f64 (+.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n))))) 2) (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n))))) 2))) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n))))))
(pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k)))))) 2)) 2) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k)))))))
(neg.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 (neg.f64 k) n)))
(/.f64 (.f64 (.f64 (PI.f64) -2) 1) (/.f64 (neg.f64 k) n))
(.f64 (PI.f64) (.f64 -2 (/.f64 n (neg.f64 k))))
(sqrt.f64 (pow.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64))) -2))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(.f64 n (.f64 (PI.f64) (/.f64 2 k)))
(log.f64 (pow.f64 (exp.f64 n) (/.f64 (*.f64 2 (PI.f64)) k)))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(.f64 n (.f64 (PI.f64) (/.f64 2 k)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(.f64 n (.f64 (PI.f64) (/.f64 2 k)))
(cbrt.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(.f64 n (.f64 (PI.f64) (/.f64 2 k)))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) 3) (pow.f64 (/.f64 n k) -3)))
(cbrt.f64 (/.f64 (*.f64 8 (pow.f64 (PI.f64) 3)) (pow.f64 (/.f64 n k) -3)))
(expm1.f64 (log1p.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(.f64 n (.f64 (PI.f64) (/.f64 2 k)))
(log1p.f64 (expm1.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(.f64 n (.f64 (PI.f64) (/.f64 2 k)))
(exp.f64 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(.f64 n (.f64 (PI.f64) (/.f64 2 k)))

localize29.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.2b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.3b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))

Compiler

Compiled 53 to 38 computations (28.3% saved)

series513.0ms (0.6%)

Counts

1 → 16

Calls

6 calls:

Time	Variable		Point	Expression
268.0ms	k	@	-inf	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
239.0ms	n	@	-inf	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
2.0ms	k	@	0	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
1.0ms	n	@	inf	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
1.0ms	n	@	0	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Compiler

Compiled 57828 to 51592 computations (10.8% saved)

rewrite56.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

723×	`log-prod_binary64`
505×	`pow-unpow_binary64`
387×	`pow2_binary64`
265×	`pow1/3_binary64`
261×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	23
1	307	23
2	3794	22

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

Inputs
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (pow.f64 k -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3) (pow.f64 (pow.f64 k -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))) 1))))))

simplify54.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

558×	`associate-+l+_binary64`
536×	`unswap-sqr_binary64`
428×	`fma-def_binary64`
396×	`log-prod_binary64`
314×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	118	1290
1	316	1260
2	1170	1027
3	4899	924

Stop Event

1×	node limit

Counts

37 → 55

Calls

Call 1

Inputs
(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/2) (pow.f64 k -1/2))
(+.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (pow.f64 k -1/2)) (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(+.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (pow.f64 k -1/2)) (+.f64 (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 1/2 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))))))
(+.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (pow.f64 k -1/2)) (+.f64 (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2))))) (.f64 1/6 (.f64 (pow.f64 k -1/2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k 3) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64))))) 3))))))))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) (pow.f64 (/.f64 1 k) 1/2))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) (pow.f64 (/.f64 1 k) 1/2))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) (pow.f64 (/.f64 1 k) 1/2))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) (pow.f64 (/.f64 1 k) 1/2))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (pow.f64 k -1/2))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (pow.f64 k -1/2))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (pow.f64 k -1/2))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (pow.f64 k -1/2))
(.f64 (pow.f64 k -1/2) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (pow.f64 k -1/2) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (pow.f64 k -1/2) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (pow.f64 k -1/2) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(+.f64 0 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))) 1)
(pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 1)
(pow.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)) 1/2)
(pow.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 3) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))) 3)
(pow.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (pow.f64 k -1/4)) 2)
(pow.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)) 1/3)
(pow.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))
(log.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))))
(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 3))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))) 1))

Outputs
(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/2) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2))
(+.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (pow.f64 k -1/2)) (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(fma.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (pow.f64 k -1/2) (.f64 -1/2 (.f64 (.f64 k (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n))) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 (.f64 2 (PI.f64)) n))))))
(fma.f64 -1/2 (.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) k)) (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (+.f64 (pow.f64 k -1/2) (.f64 (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (.f64 k -1/2))))
(+.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (pow.f64 k -1/2)) (+.f64 (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 1/2 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))))))
(fma.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (pow.f64 k -1/2) (fma.f64 -1/2 (.f64 (.f64 k (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n))) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 (.f64 2 (PI.f64)) n)))) (.f64 (.f64 1/2 (.f64 k k)) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (pow.f64 k -1/2)) (pow.f64 (.f64 -1/2 (log.f64 (.f64 (*.f64 2 (PI.f64)) n))) 2)))))
(fma.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2) (fma.f64 1/2 (.f64 k (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)) (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))))
(fma.f64 1/2 (.f64 k (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (+.f64 (pow.f64 k -1/2) (.f64 (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (*.f64 k -1/2)))))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (+.f64 (pow.f64 k -1/2) (+.f64 (.f64 (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (.f64 k -1/2)) (.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)) (.f64 1/2 (*.f64 k k))))))
(+.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (pow.f64 k -1/2)) (+.f64 (.f64 -1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2))))) (.f64 1/6 (.f64 (pow.f64 k -1/2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2) (.f64 (pow.f64 k 3) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64))))) 3))))))))
(fma.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (pow.f64 k -1/2) (fma.f64 -1/2 (.f64 (.f64 k (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n))) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 (.f64 2 (PI.f64)) n)))) (fma.f64 1/2 (.f64 (.f64 k k) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (pow.f64 k -1/2)) (pow.f64 (.f64 -1/2 (log.f64 (.f64 (.f64 2 (PI.f64)) n))) 2))) (.f64 (.f64 1/6 (pow.f64 k -1/2)) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (pow.f64 k 3)) (.f64 -1/8 (pow.f64 (log.f64 (.f64 (*.f64 2 (PI.f64)) n)) 3)))))))
(fma.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2) (fma.f64 -1/2 (.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) k)) (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (pow.f64 k -1/2) (.f64 (.f64 (pow.f64 k 3) -1/8) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)) (.f64 1/2 (*.f64 k k))))))
(+.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (+.f64 (pow.f64 k -1/2) (.f64 (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (.f64 k -1/2)))) (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (+.f64 (.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)) (.f64 1/2 (.f64 k k))) (.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (.f64 (pow.f64 k 3) -1/8)) (.f64 (pow.f64 k -1/2) 1/6)))))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (+.f64 (+.f64 (.f64 (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (.f64 k -1/2)) (.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)) (.f64 1/2 (.f64 k k)))) (+.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (.f64 (pow.f64 k 3) -1/8)) (*.f64 (pow.f64 k -1/2) 1/6)) (pow.f64 k -1/2))))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) (pow.f64 (/.f64 1 k) 1/2))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) (pow.f64 (/.f64 1 k) 1/2))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) (pow.f64 (/.f64 1 k) 1/2))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) (pow.f64 (/.f64 1 k) 1/2))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (pow.f64 k -1/2))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (pow.f64 k -1/2))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (pow.f64 k -1/2))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (pow.f64 k -1/2))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (pow.f64 k -1/2) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (pow.f64 k -1/2) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (pow.f64 k -1/2) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(.f64 (pow.f64 k -1/2) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(+.f64 0 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 1 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (-.f64 1 k)))))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 1 k) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 1 k) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 1 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (-.f64 1 k))))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 1 k) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))) 1)
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 1)
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)) 1/2)
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 3) 1/3)
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))) 3)
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (pow.f64 k -1/4)) 2)
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)) 1/3)
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) n)) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (/.f64 (pow.f64 k -1/2) k) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (pow.f64 k -1/2) (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) 3) k)))
(pow.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) n)) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (/.f64 (pow.f64 k -1/2) k) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (pow.f64 k -1/2) (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) 3) k)))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(log.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 3))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) n)) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (/.f64 (pow.f64 k -1/2) k) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (pow.f64 k -1/2) (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) 3) k)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) n)) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (/.f64 (pow.f64 k -1/2) k) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (pow.f64 k -1/2) (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) 3) k)))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(exp.f64 (log.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))) 1))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))

localize36.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (pow.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) -1/2))
✓	0.2b	(.f64 (.f64 2 n) (PI.f64))
✓	0.2b	(.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) -1/2)))
✓	0.2b	(pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))

Compiler

Compiled 72 to 52 computations (27.8% saved)

series1.0s (1.2%)

Counts

4 → 68

Calls

21 calls:

Time	Variable		Point	Expression
312.0ms	k	@	-inf	(.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) -1/2)))
264.0ms	n	@	-inf	(.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) -1/2)))
199.0ms	n	@	-inf	(/.f64 1 (pow.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) -1/2))
151.0ms	n	@	-inf	(pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))
20.0ms	n	@	0	(.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) -1/2)))

Compiler

Compiled 100584 to 89838 computations (10.7% saved)

rewrite75.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

794×	`log-prod_binary64`
413×	`pow2_binary64`
277×	`pow1/3_binary64`
273×	`expm1-udef_binary64`
272×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	62
1	336	60
2	4241	60

Stop Event

1×	node limit

Counts

4 → 144

Calls

Call 1

Inputs
(pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))
(.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) -1/2)))
(.f64 (.f64 2 n) (PI.f64))
(/.f64 1 (pow.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) -1/2))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (.f64 n (PI.f64))) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) 2) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/4) (.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/4) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (pow.f64 (PI.f64) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (PI.f64) (-.f64 1 k)) (pow.f64 (+.f64 n n) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/4) 3) (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 (-.f64 1 k)) (pow.f64 (.f64 n (PI.f64)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 (-.f64 1 k)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 n (PI.f64)) 2))) (-.f64 1 k)) (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x 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pow.f64 (neg.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (-.f64 1 k) -1/2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1/2 (/.f64 k 2)) 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/2 (/.f64 k 2))))))))

simplify115.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

416×	`associate-r_binary64`
355×	`associate-l_binary64`
337×	`log-prod_binary64`
266×	`cube-prod_binary64`
206×	`exp-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	499	6528
1	1288	5567
2	5742	5505

Stop Event

1×	node limit

Counts

212 → 248

Calls

Call 1

Inputs
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(.f64 2 (.f64 n (PI.f64)))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 2 (.f64 n (PI.f64))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 n (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 -1 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2) (PI.f64)))) (.f64 2 (.f64 n (PI.f64)))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 1/3 (.f64 n (.f64 (pow.f64 (.f64 -1 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 3) (.f64 (pow.f64 k 3) (PI.f64))))) (+.f64 (.f64 n (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 -1 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2) (PI.f64)))) (.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2))
(+.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)) (.f64 -1/2 (/.f64 (.f64 k (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2))))
(+.f64 (.f64 -1 (.f64 (+.f64 (/.f64 (.f64 (+.f64 (.f64 1/2 (pow.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)) (.f64 -1/4 (+.f64 (.f64 -1 (/.f64 (pow.f64 (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64)))) 2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 2))) (pow.f64 (.f64 -1 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (pow.f64 k -1/2)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)) (.f64 -1/4 (/.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (pow.f64 k -1/2)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)))) (pow.f64 k 2))) (+.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)) (.f64 -1/2 (/.f64 (.f64 k (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)))))
(+.f64 (.f64 -1 (.f64 (+.f64 (/.f64 (.f64 (+.f64 (.f64 1/2 (pow.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)) (.f64 -1/4 (+.f64 (.f64 -1 (/.f64 (pow.f64 (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64)))) 2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 2))) (pow.f64 (.f64 -1 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (pow.f64 k -1/2)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)) (.f64 -1/4 (/.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (pow.f64 k -1/2)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)))) (pow.f64 k 2))) (+.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 k (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2))) (.f64 -1 (.f64 (+.f64 (/.f64 (.f64 (pow.f64 k -1/2) (+.f64 (.f64 -1/8 (.f64 (+.f64 (.f64 -1 (/.f64 (pow.f64 (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64)))) 2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 2))) (pow.f64 (.f64 -1 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (+.f64 (.f64 -1/12 (+.f64 (pow.f64 (.f64 -1 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 3) (+.f64 (.f64 12 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 (PI.f64) 2) (.f64 (pow.f64 (.f64 -1 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 2))) (.f64 2 (/.f64 (pow.f64 (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64)))) 3) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3)))))) (.f64 1/6 (pow.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 3))))) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (.f64 1/2 (pow.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)) (.f64 -1/4 (+.f64 (.f64 -1 (/.f64 (pow.f64 (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64)))) 2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 2))) (pow.f64 (.f64 -1 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2))) (.f64 -1/2 (.f64 (+.f64 (.f64 -1/4 (/.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2))) (/.f64 (.f64 (+.f64 (.f64 -1/4 (+.f64 (pow.f64 (.f64 -1 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2) (.f64 -1 (/.f64 (pow.f64 (.f64 -2 (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 2))))) (.f64 1/2 (pow.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2))) (pow.f64 k -1/2)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))) (pow.f64 k 3))))))
(/.f64 (pow.f64 (/.f64 1 k) 1/2) (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) -1/2))
(/.f64 (pow.f64 (/.f64 1 k) 1/2) (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) -1/2))
(/.f64 (pow.f64 (/.f64 1 k) 1/2) (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) -1/2))
(/.f64 (pow.f64 (/.f64 1 k) 1/2) (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) -1/2))
(/.f64 (pow.f64 k -1/2) (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 (pow.f64 k -1/2) (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 (pow.f64 k -1/2) (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 (pow.f64 k -1/2) (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 (pow.f64 k -1/2) (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 (pow.f64 k -1/2) (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 (pow.f64 k -1/2) (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 (pow.f64 k -1/2) (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(/.f64 1 (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 1 (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 1 (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 1 (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 1 (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 1 (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 1 (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 1 (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2))
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(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))) 1)
(.f64 1 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 1)
(.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))) (cbrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))
(.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/4) (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/4))
(.f64 -1 (/.f64 1 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (-.f64 1 k) -1/2)))))
(*.f64 (sqrt.f64 (pow.f64 (+.f64 n n) (-.f64 1 k))) (sqrt.f64 (pow.f64 (PI.f64) (-.f64 1 k))))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) 2)) (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) 2) 1/2) (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 1/2))
(*.f64 (pow.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) 1/2) (pow.f64 (pow.f64 (PI.f64) (-.f64 1 k)) 1/2))
(.f64 (pow.f64 2 (-.f64 1/2 (/.f64 k 2))) (pow.f64 (.f64 n (PI.f64)) (-.f64 1/2 (/.f64 k 2))))
(*.f64 (pow.f64 (+.f64 n n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (PI.f64) (-.f64 1/2 (/.f64 k 2))))
(*.f64 (pow.f64 (PI.f64) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (+.f64 n n) (-.f64 1/2 (/.f64 k 2))))
(.f64 (pow.f64 1 (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(.f64 (pow.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 n (PI.f64)) 2))) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (cbrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/2 (/.f64 k 2))))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/2 (/.f64 k 2))))
(.f64 (/.f64 1 (cbrt.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) -1))) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))
(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1/2 (/.f64 k 2)) 2)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (/.f64 (-.f64 1/2 (/.f64 k 2)) 2)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (neg.f64 (*.f64 (-.f64 1 k) -1/2)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (.f64 (-.f64 1 k) -1/2) -1))
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2)
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)) -1)
(pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) 1)
(pow.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) 3) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))) 3)
(pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/4) 2)
(pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1/2 (/.f64 k 2))) 2)
(pow.f64 (neg.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))) -1)
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1/2 (/.f64 k 2)) 2)) 2)
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(fabs.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(log.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))))
(cbrt.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) 3))
(expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(exp.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))) 1/2))
(exp.f64 (.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))) -1))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) 1))
(exp.f64 (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/2 (/.f64 k 2))))

Outputs
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 2 (.f64 n (PI.f64))))
(fma.f64 -2 (.f64 k (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 2 (*.f64 n (PI.f64))))
(fma.f64 2 (.f64 n (PI.f64)) (.f64 k (.f64 (.f64 (.f64 n (PI.f64)) -2) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 n (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 -1 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2) (PI.f64)))) (.f64 2 (.f64 n (PI.f64)))))
(fma.f64 -2 (.f64 k (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (fma.f64 n (.f64 (.f64 (.f64 k k) (pow.f64 (neg.f64 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)) (PI.f64)) (.f64 2 (.f64 n (PI.f64)))))
(fma.f64 -2 (.f64 k (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))) (fma.f64 n (.f64 (PI.f64) (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (.f64 n (.f64 2 (PI.f64)))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 1/3 (.f64 n (.f64 (pow.f64 (.f64 -1 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 3) (.f64 (pow.f64 k 3) (PI.f64))))) (+.f64 (.f64 n (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 -1 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2) (PI.f64)))) (.f64 2 (*.f64 n (PI.f64))))))
(fma.f64 -2 (.f64 k (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (fma.f64 1/3 (.f64 n (.f64 (pow.f64 (neg.f64 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 3) (.f64 (PI.f64) (pow.f64 k 3)))) (fma.f64 n (.f64 (.f64 (.f64 k k) (pow.f64 (neg.f64 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)) (PI.f64)) (.f64 2 (*.f64 n (PI.f64))))))
(fma.f64 -2 (.f64 k (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))) (fma.f64 1/3 (.f64 (pow.f64 (neg.f64 (log.f64 (.f64 n (.f64 2 (PI.f64))))) 3) (.f64 (.f64 (PI.f64) (pow.f64 k 3)) n)) (fma.f64 n (.f64 (PI.f64) (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2))
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) -1/2))
(+.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)) (.f64 -1/2 (/.f64 (.f64 k (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2))))
(+.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)) (.f64 -1/2 (/.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2))))))
(fma.f64 -1/2 (/.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k -1/2)) (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) -1/2) k)) (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) -1/2)))
(fma.f64 -1/2 (/.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) -1/2) (log.f64 (.f64 n (.f64 2 (PI.f64)))))) (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) -1/2)))
(+.f64 (.f64 -1 (.f64 (+.f64 (/.f64 (.f64 (+.f64 (.f64 1/2 (pow.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)) (.f64 -1/4 (+.f64 (.f64 -1 (/.f64 (pow.f64 (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64)))) 2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 2))) (pow.f64 (.f64 -1 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (pow.f64 k -1/2)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)) (.f64 -1/4 (/.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (pow.f64 k -1/2)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)))) (pow.f64 k 2))) (+.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)) (.f64 -1/2 (/.f64 (.f64 k (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)))))
(fma.f64 -1 (.f64 (.f64 k k) (fma.f64 -1/4 (/.f64 (pow.f64 k -1/2) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (/.f64 (fma.f64 -1/4 (fma.f64 -1 (/.f64 (pow.f64 (.f64 -2 (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) 2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 2)) (pow.f64 (neg.f64 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)) (.f64 1/2 (pow.f64 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 1/2) 2))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2) (pow.f64 k -1/2))))) (+.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)) (.f64 -1/2 (/.f64 k (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2) (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2)))))))
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(/.f64 (.f64 1 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))) (cbrt.f64 (/.f64 1 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))
(/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))) (cbrt.f64 (/.f64 1 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1/2 (/.f64 k 2)) 2)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (/.f64 (-.f64 1/2 (/.f64 k 2)) 2)))
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (neg.f64 (*.f64 (-.f64 1 k) -1/2)))
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (.f64 (-.f64 1 k) -1/2) -1))
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2)
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)) -1)
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) 1)
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(pow.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) 3) 1/3)
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(pow.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))) 3)
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/4) 2)
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1/2 (/.f64 k 2))) 2)
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))
(pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k))
(pow.f64 (neg.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))) -1)
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1/2 (/.f64 k 2)) 2)) 2)
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(fabs.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(log.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))))
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(cbrt.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) 3))
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(exp.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(exp.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))) 1/2))
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(exp.f64 (.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))) -1))
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) 1))
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(exp.f64 (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/2 (/.f64 k 2))))
(exp.f64 (neg.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) -1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))

eval556.0ms (0.7%)

Compiler: Compiled 31417 to 20923 computations (33.4% saved)

prune323.0ms (0.4%)

Pruning

33 alts after pruning (29 fresh and 4 done)

	Pruned	Kept	Total
New	1194	19	1213
Fresh	20	10	30
Picked	1	0	1
Done	4	4	8
Total	1219	33	1252

Error

Counts

1252 → 33

Alt Table

Click to see full alt table

Status	Error	Program
	40.1b	(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2) 1/3)
	35.2b	(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/6) 3)
	10.5b	(pow.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))) -1/2)
	32.7b	(pow.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64)))) -1/2)
	10.3b	(pow.f64 (.f64 (/.f64 k 2) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k) (.f64 n (PI.f64)))) -1/2)
▶	33.0b	(pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 3/2)
✓	0.4b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	22.9b	(/.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 3/2) (sqrt.f64 k))
▶	0.4b	(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
✓	0.3b	(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 n 2) (PI.f64))) (pow.f64 (.f64 (.f64 n 2) (PI.f64)) (.f64 k -1/2))) (sqrt.f64 k))
✓	22.6b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
	0.4b	(/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)) (pow.f64 k -1/2)))
	22.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))))
▶	10.6b	(/.f64 1 (/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))))
▶	32.7b	(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64)))))
	0.5b	(.f64 (pow.f64 k -1/2) (.f64 -1 (/.f64 1 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))))))
	22.7b	(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))))
	22.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
	32.9b	(.f64 (sqrt.f64 (.f64 n (/.f64 2 k))) (sqrt.f64 (PI.f64)))
	33.0b	(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 (/.f64 n k)))
	22.9b	(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 2 (/.f64 k (PI.f64)))))
	10.6b	(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))
	32.8b	(sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k))
	10.4b	(sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k))
	32.7b	(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
	32.8b	(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
	10.4b	(sqrt.f64 (/.f64 2 (/.f64 k (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) k)))))
	32.8b	(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)))
	33.0b	(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))))
	12.9b	(sqrt.f64 (.f64 n (-.f64 (+.f64 1 (.f64 (/.f64 2 k) (PI.f64))) 1)))
▶	32.8b	(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
✓	34.7b	(exp.f64 (.f64 (log.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))) 1/2))
	38.4b	(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)) 3/2))

Compiler

Compiled 843 to 683 computations (19% saved)

localize29.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	0.3b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 (-.f64 1 k) -1/2))

Compiler

Compiled 53 to 38 computations (28.3% saved)

series767.0ms (0.9%)

Counts

2 → 36

Calls

12 calls:

Time	Variable		Point	Expression
288.0ms	n	@	-inf	(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
270.0ms	k	@	-inf	(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
188.0ms	n	@	-inf	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 (-.f64 1 k) -1/2))
5.0ms	n	@	0	(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
4.0ms	k	@	0	(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))

Compiler

Compiled 79933 to 71530 computations (10.5% saved)

rewrite77.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

760×	`log-prod_binary64`
394×	`pow2_binary64`
266×	`pow1/3_binary64`
263×	`expm1-udef_binary64`
262×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	40
1	305	40
2	3873	40

Stop Event

1×	node limit

Counts

2 → 65

Calls

Call 1

Inputs
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 (-.f64 1 k) -1/2))
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 (-.f64 1 k) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 (-.f64 1 k) -1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 (-.f64 1 k) -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 (-.f64 1 k) -1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 (-.f64 1 k) -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 (-.f64 1 k) -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 (-.f64 1 k) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 (-.f64 1 k) -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 (-.f64 1 k) -1/2))) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) -1)) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 (-.f64 1 k) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 n (*.f64 (-.f64 1 k) -1/2)) (pow.f64 (*.f64 2 (PI.f64)) (*.f64 (-.f64 1 k) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 (-.f64 1 k) -1/2)) (pow.f64 n (*.f64 (-.f64 1 k) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (/.f64 (-.f64 1 k) -4)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (/.f64 (-.f64 1 k) -4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 (*.f64 (-.f64 1 k) -1/2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 (-.f64 1 k) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) 2) (*.f64 (-.f64 1 k) -1/2)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 (-.f64 1 k) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 (-.f64 1 k) -1/2)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 (-.f64 1 k) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n 2) (*.f64 (-.f64 1 k) -1/2)) (pow.f64 (PI.f64) (*.f64 (-.f64 1 k) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 (-.f64 1 k) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 (-.f64 1 k) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 (-.f64 1 k) -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 (-.f64 1 k) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 (-.f64 1 k) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 -1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))) -1/2))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 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(#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 k -1)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (/.f64 (-.f64 1 k) -4))) (/.f64 (cbrt.f64 (pow.f64 k -1/2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (/.f64 (-.f64 1 k) -4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 n (*.f64 (-.f64 1 k) -1/2))) (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (PI.f64)) (*.f64 (-.f64 1 k) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 k -1)) (pow.f64 n (*.f64 (-.f64 1 k) -1/2))) (/.f64 (cbrt.f64 (pow.f64 k -1/2)) (pow.f64 (*.f64 2 (PI.f64)) (*.f64 (-.f64 1 k) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 k -1/4) (pow.f64 n (*.f64 (-.f64 1 k) -1/2))) (/.f64 (pow.f64 k -1/4) (pow.f64 (*.f64 2 (PI.f64)) (*.f64 (-.f64 1 k) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2)) 1)))) (#(struct:change #<rule egg-rr> 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simplify69.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

747×	`associate-/l*_binary64`
690×	`fma-def_binary64`
548×	`unswap-sqr_binary64`
538×	`associate-/r*_binary64`
374×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	265	3371
1	687	3028
2	2666	2910

Stop Event

1×	node limit

Counts

101 → 147

Calls

Call 1

Inputs
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)
(+.f64 (.f64 1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2))
(+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)))) (+.f64 (.f64 1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2)))
(+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)))) (+.f64 (.f64 1/6 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2) (.f64 (pow.f64 k 3) (pow.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 3)))) (+.f64 (.f64 1/2 (.f64 k (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2))
(+.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)) (.f64 -1/2 (/.f64 (.f64 k (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2))))
(+.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 k (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2))) (.f64 -1 (.f64 (+.f64 (.f64 -1/4 (/.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (pow.f64 k -1/2)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2))) (.f64 1/2 (/.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)))) (pow.f64 k 2)))))
(+.f64 (.f64 -1 (.f64 (+.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 -1/4 (/.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2))) (.f64 1/2 (/.f64 (.f64 (pow.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2) (pow.f64 k -1/2)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (pow.f64 k -1/2) (.f64 (pow.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2))) (.f64 1/6 (/.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 3)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2))))) (pow.f64 k 3))) (+.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 k (.f64 (pow.f64 k -1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2))) (.f64 -1 (.f64 (+.f64 (.f64 -1/4 (/.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (pow.f64 k -1/2)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2))) (.f64 1/2 (/.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)))) (pow.f64 k 2))))))
(/.f64 (pow.f64 (/.f64 1 k) 1/2) (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))))
(/.f64 (pow.f64 (/.f64 1 k) 1/2) (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))))
(/.f64 (pow.f64 (/.f64 1 k) 1/2) (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))))
(/.f64 (pow.f64 (/.f64 1 k) 1/2) (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))))
(/.f64 (pow.f64 k -1/2) (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(/.f64 (pow.f64 k -1/2) (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(/.f64 (pow.f64 k -1/2) (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(/.f64 (pow.f64 k -1/2) (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(/.f64 (pow.f64 k -1/2) (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 (pow.f64 k -1/2) (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 (pow.f64 k -1/2) (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 (pow.f64 k -1/2) (exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))
(+.f64 0 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/2))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/2)))) 1)
(.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/2)) 1)
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/2))) (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) -1)))
(.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) -1)) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/2))))
(.f64 (pow.f64 n (.f64 (-.f64 1 k) -1/2)) (pow.f64 (.f64 2 (PI.f64)) (.f64 (-.f64 1 k) -1/2)))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 (-.f64 1 k) -1/2)) (pow.f64 n (.f64 (-.f64 1 k) -1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (/.f64 (-.f64 1 k) -4)) (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (/.f64 (-.f64 1 k) -4)))
(.f64 (pow.f64 1 (.f64 (-.f64 1 k) -1/2)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/2)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 2) (.f64 (-.f64 1 k) -1/2)) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) (*.f64 (-.f64 1 k) -1/2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 (-.f64 1 k) -1/2)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (*.f64 (-.f64 1 k) -1/2)))
(.f64 (pow.f64 (.f64 n 2) (.f64 (-.f64 1 k) -1/2)) (pow.f64 (PI.f64) (.f64 (-.f64 1 k) -1/2)))
(sqrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) -1))
(log.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/2))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/2)))))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/2)) 3))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/2))))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/2))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (.f64 n 2))))))
(exp.f64 (.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (*.f64 n 2))))) 1))
(exp.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (.f64 n 2)))) -1/2))
(+.f64 0 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) 1/2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) 1/2)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) 1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) 1/2)))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2)))) 1)
(.f64 1 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) 1/2)))
(.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2))
(.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) 1/2)) 1)
(.f64 (cbrt.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) 1/2))) (cbrt.f64 (/.f64 (pow.f64 k -1) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) -1))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 k -1) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) -1))) (cbrt.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) 1/2))))
(.f64 (cbrt.f64 (pow.f64 k -1)) (.f64 (cbrt.f64 (pow.f64 k -1/2)) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) 1/2)))
(.f64 (/.f64 (pow.f64 k -1/4) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (/.f64 (-.f64 1 k) -4))) (/.f64 (pow.f64 k -1/4) (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (/.f64 (-.f64 1 k) -4))))
(.f64 (neg.f64 (pow.f64 k -1/2)) (/.f64 1 (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/2)))))
(.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2) (pow.f64 k -1/2))
(.f64 (pow.f64 k -1/4) (.f64 (pow.f64 k -1/4) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) 1/2)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 k -1)) 1) (/.f64 (cbrt.f64 (pow.f64 k -1/2)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/2))))
(.f64 (/.f64 (pow.f64 k -1/4) 1) (/.f64 (pow.f64 k -1/4) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/2))))
(.f64 (/.f64 1 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) -1))) (/.f64 (pow.f64 k -1/2) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/2)))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 k -1)) (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) -1))) (cbrt.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) 1/2))))
(.f64 (/.f64 (pow.f64 k -1/4) (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) -1))) (/.f64 (pow.f64 k -1/4) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/2)))))
(.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (/.f64 (-.f64 1 k) -4))) (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (/.f64 (-.f64 1 k) -4))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 k -1)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (/.f64 (-.f64 1 k) -4))) (/.f64 (cbrt.f64 (pow.f64 k -1/2)) (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (/.f64 (-.f64 1 k) -4))))
(.f64 (/.f64 1 (pow.f64 n (.f64 (-.f64 1 k) -1/2))) (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (PI.f64)) (.f64 (-.f64 1 k) -1/2))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 k -1)) (pow.f64 n (.f64 (-.f64 1 k) -1/2))) (/.f64 (cbrt.f64 (pow.f64 k -1/2)) (pow.f64 (.f64 2 (PI.f64)) (.f64 (-.f64 1 k) -1/2))))
(.f64 (/.f64 (pow.f64 k -1/4) (pow.f64 n (.f64 (-.f64 1 k) -1/2))) (/.f64 (pow.f64 k -1/4) (pow.f64 (.f64 2 (PI.f64)) (.f64 (-.f64 1 k) -1/2))))
(pow.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2)) 1)
(pow.f64 (pow.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2)) 3) 1/3)
(pow.f64 (cbrt.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2))) 3)
(pow.f64 (/.f64 (pow.f64 k -1/4) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (/.f64 (-.f64 1 k) -4))) 2)
(pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/2)) (pow.f64 k -1/2)) -1)
(pow.f64 (/.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/2)) 3)) 1/3)
(pow.f64 (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/2)) (pow.f64 k -1/2)) 1) -1)
(neg.f64 (/.f64 (pow.f64 k -1/2) (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/2)))))
(sqrt.f64 (/.f64 (pow.f64 k -1) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) -1)))
(log.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2)))))
(cbrt.f64 (pow.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2)) 3))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/2)) 3)))
(expm1.f64 (log1p.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2))))
(log1p.f64 (expm1.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2))))
(exp.f64 (log.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2))))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) 1/2))) 1))

Outputs
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 -1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) -1/2)
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 -1/2 (-.f64 1 k)))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 -1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) -1/2)
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 -1/2 (-.f64 1 k)))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 -1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) -1/2)
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 -1/2 (-.f64 1 k)))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 -1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) -1/2)
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 -1/2 (-.f64 1 k)))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 -1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) -1/2)
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 -1/2 (-.f64 1 k)))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 -1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) -1/2)
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 -1/2 (-.f64 1 k)))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 -1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) -1/2)
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 -1/2 (-.f64 1 k)))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 -1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
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(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2)))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
(cbrt.f64 (pow.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2)) 3))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/2)) 3)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 -1/2 (-.f64 1 k))) 3)))
(cbrt.f64 (/.f64 (/.f64 (pow.f64 k -1/2) k) (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 -1/2 (-.f64 1 k))) 3)))
(cbrt.f64 (/.f64 (pow.f64 k -1/2) (.f64 (pow.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 -1/4 (/.f64 k -4))) 6) k)))
(expm1.f64 (log1p.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
(log1p.f64 (expm1.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
(exp.f64 (log.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) 1/2))) 1))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))

localize10.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 k (PI.f64))
✓	0.2b	(/.f64 n (/.f64 k (PI.f64)))
✓	9.8b	(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))

Compiler

Compiled 29 to 11 computations (62.1% saved)

series2.3s (2.8%)

Counts

3 → 24

Calls

15 calls:

Time	Variable		Point	Expression
461.0ms	n	@	-inf	(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
421.0ms	k	@	-inf	(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
385.0ms	k	@	inf	(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
365.0ms	n	@	0	(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
356.0ms	n	@	inf	(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))

Compiler

Compiled 260360 to 164044 computations (37% saved)

rewrite63.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

537×	`log-prod_binary64`
411×	`exp-prod_binary64`
284×	`pow-prod-down_binary64`
250×	`pow2_binary64`
223×	`pow-unpow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	195	26
2	2641	26

Stop Event

1×	node limit

Counts

3 → 149

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 k (PI.f64))

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 n (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (/.f64 (PI.f64) k))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (/.f64 (PI.f64) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (/.f64 (PI.f64) k)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (/.f64 (PI.f64) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 n (/.f64 (PI.f64) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 n (/.f64 (PI.f64) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (PI.f64) (/.f64 n k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 n (/.f64 (PI.f64) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 n (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 n) 2) (*.f64 (cbrt.f64 n) (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (cbrt.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) 2)) (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 n) (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 n) (/.f64 1 (/.f64 (neg.f64 k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) k) n)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 n k) (PI.f64))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 n) 2) 1) (/.f64 (cbrt.f64 n) (/.f64 k (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 n) 1) (/.f64 (sqrt.f64 n) (/.f64 k (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) 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k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 n (/.f64 (PI.f64) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 k (*.f64 n (PI.f64))) -3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 n 3) (pow.f64 (/.f64 k (PI.f64)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 n (/.f64 (PI.f64) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 n (/.f64 (PI.f64) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 n (/.f64 (PI.f64) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (PI.f64) k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 k (*.f64 n (PI.f64))) -3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 k (*.f64 n (PI.f64)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (PI.f64) k))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 n) 1) (log.f64 (/.f64 k (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 n) (*.f64 (log.f64 (/.f64 k (PI.f64))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 n) 1) (*.f64 (log.f64 (/.f64 k (PI.f64))) 1)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 k (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 k (PI.f64)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 k (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 k (PI.f64))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 k (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 k (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 k (/.f64 1 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 k (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 k (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 k (PI.f64))) (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) 2) (cbrt.f64 (/.f64 k (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 k k)) (*.f64 (cbrt.f64 k) (/.f64 1 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (/.f64 k (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 k) (/.f64 1 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 k) (/.f64 1 (neg.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (PI.f64)) k)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 k k)) 1) (/.f64 (cbrt.f64 k) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 k) 1) (/.f64 (sqrt.f64 k) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (PI.f64)) -2) (/.f64 k (cbrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 k k)) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (/.f64 k (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 k) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (/.f64 (sqrt.f64 k) (cbrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) -1/2) (/.f64 k (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 k k)) (sqrt.f64 (PI.f64))) (/.f64 (cbrt.f64 k) (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 k (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 k (PI.f64)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 k (PI.f64)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 k (PI.f64))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (PI.f64) k) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (/.f64 k (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 k 3) (pow.f64 (PI.f64) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (PI.f64) k) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 k (PI.f64)))) 2)) (cbrt.f64 (log.f64 (/.f64 k (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 k (PI.f64))))) (sqrt.f64 (log.f64 (/.f64 k (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 k (neg.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 k (PI.f64)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 k (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 k (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 k (PI.f64)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 k 3) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 k (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 k (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 k (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 k (PI.f64))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (/.f64 k (PI.f64)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 k (PI.f64)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 k (PI.f64)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (PI.f64) k)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 k (PI.f64))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 k) 1) (log.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 k) (*.f64 (log.f64 (PI.f64)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 k) 1) (*.f64 (log.f64 (PI.f64)) 1)))))))

simplify60.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

480×	`fma-def_binary64`
399×	`unswap-sqr_binary64`
290×	`distribute-rgt-in_binary64`
277×	`distribute-lft-in_binary64`
272×	`log-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	360	1834
1	829	1775
2	2379	1775

Stop Event

1×	node limit

Counts

173 → 185

Calls

Call 1

Inputs
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(+.f64 0 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k))))) 1)
(.f64 (sqrt.f64 (.f64 (*.f64 2 n) (/.f64 (PI.f64) k))) 1)
(.f64 1 (sqrt.f64 (.f64 (*.f64 2 n) (/.f64 (PI.f64) k))))
(.f64 (cbrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k))) (pow.f64 (.f64 (*.f64 2 n) (/.f64 (PI.f64) k)) 1/6))
(.f64 (pow.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)) 1/6) (cbrt.f64 (.f64 (*.f64 2 n) (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(.f64 (pow.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)) 1/4) (pow.f64 (.f64 (*.f64 2 n) (/.f64 (PI.f64) k)) 1/4))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 2))
(/.f64 (sqrt.f64 (*.f64 2 n)) (sqrt.f64 (/.f64 k (PI.f64))))
(pow.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)) 1/2)
(pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k))) 1)
(pow.f64 (.f64 4 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 2)) 1/4)
(pow.f64 (pow.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)) 3) 1/6)
(pow.f64 (pow.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)) 3/2) 1/3)
(pow.f64 (cbrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k))) 3/2)
(pow.f64 (pow.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)) 1/6) 3)
(pow.f64 (pow.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)) 1/4) 2)
(pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)))))
(pow.f64 (exp.f64 1/2) (log.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k))))))
(fabs.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k))))))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 2 n) (/.f64 (PI.f64) k))) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 2 n) (/.f64 (PI.f64) k)))) 1))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 2 n) (/.f64 (PI.f64) k)) 3/2)) 1/3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 2 n) (/.f64 (PI.f64) k)) 1/6)) 3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 2 n) (/.f64 (PI.f64) k)) 1/4)) 2))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k))) 1) 1/2))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k))) 1/2) 1))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)))) 1) 1))
(+.f64 0 (*.f64 n (/.f64 (PI.f64) k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (/.f64 (PI.f64) k))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (/.f64 (PI.f64) k)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (/.f64 (PI.f64) k)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (/.f64 (PI.f64) k)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 n (/.f64 (PI.f64) k)))) 1)
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (PI.f64) (/.f64 n k))
(.f64 (.f64 n (/.f64 (PI.f64) k)) 1)
(.f64 1 (.f64 n (/.f64 (PI.f64) k)))
(.f64 (pow.f64 (cbrt.f64 n) 2) (.f64 (cbrt.f64 n) (/.f64 (PI.f64) k)))
(.f64 (cbrt.f64 (.f64 n (/.f64 (PI.f64) k))) (cbrt.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) 2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 2)) (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (/.f64 (PI.f64) k)))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (neg.f64 n) (/.f64 1 (/.f64 (neg.f64 k) (PI.f64))))
(*.f64 (/.f64 (PI.f64) k) n)
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 n) 2) 1) (/.f64 (cbrt.f64 n) (/.f64 k (PI.f64))))
(*.f64 (/.f64 (sqrt.f64 n) 1) (/.f64 (sqrt.f64 n) (/.f64 k (PI.f64))))
(*.f64 (/.f64 (sqrt.f64 n) k) (/.f64 (sqrt.f64 n) (/.f64 1 (PI.f64))))
(*.f64 (/.f64 1 k) (/.f64 n (/.f64 1 (PI.f64))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 n) 2) k) (/.f64 (cbrt.f64 n) (/.f64 1 (PI.f64))))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) -2) (/.f64 n (cbrt.f64 (/.f64 k (PI.f64)))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 n) 2) (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) 2)) (cbrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) 2)) (/.f64 (sqrt.f64 n) (cbrt.f64 (/.f64 k (PI.f64)))))
(*.f64 (pow.f64 (/.f64 k (PI.f64)) -1/2) (/.f64 n (sqrt.f64 (/.f64 k (PI.f64)))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 n) 2) (sqrt.f64 (/.f64 k (PI.f64)))) (/.f64 (cbrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))
(*.f64 (/.f64 n 1) (/.f64 (PI.f64) k))
(*.f64 (/.f64 n (neg.f64 k)) (neg.f64 (PI.f64)))
(.f64 (.f64 (/.f64 n k) 1) (PI.f64))
(.f64 (.f64 (/.f64 n k) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) 1)
(pow.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) 2) 1/2)
(pow.f64 (pow.f64 (/.f64 k (*.f64 n (PI.f64))) -3) 1/3)
(pow.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) 3)
(pow.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) 2)
(pow.f64 (/.f64 k (*.f64 n (PI.f64))) -1)
(pow.f64 (exp.f64 1) (log.f64 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (/.f64 (pow.f64 n 3) (pow.f64 (/.f64 k (PI.f64)) 3)) 1/3)
(pow.f64 (/.f64 (/.f64 k (*.f64 n (PI.f64))) 1) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 n (/.f64 (PI.f64) k)))) 2)) (cbrt.f64 (log.f64 (.f64 n (/.f64 (PI.f64) k)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 n (/.f64 (PI.f64) k))))) (sqrt.f64 (log.f64 (.f64 n (/.f64 (PI.f64) k)))))
(neg.f64 (/.f64 n (/.f64 (neg.f64 k) (PI.f64))))
(sqrt.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) 2))
(log.f64 (pow.f64 (exp.f64 n) (/.f64 (PI.f64) k)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(cbrt.f64 (pow.f64 (/.f64 k (*.f64 n (PI.f64))) -3))
(cbrt.f64 (/.f64 (pow.f64 n 3) (pow.f64 (/.f64 k (PI.f64)) 3)))
(expm1.f64 (log1p.f64 (*.f64 n (/.f64 (PI.f64) k))))
(log1p.f64 (expm1.f64 (*.f64 n (/.f64 (PI.f64) k))))
(exp.f64 (log.f64 (*.f64 n (/.f64 (PI.f64) k))))
(exp.f64 (.f64 (log.f64 (.f64 n (/.f64 (PI.f64) k))) 1))
(exp.f64 (.f64 (log.f64 (pow.f64 (/.f64 k (.f64 n (PI.f64))) -3)) 1/3))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 n (/.f64 (PI.f64) k)))) 3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k)))) 2))
(exp.f64 (.f64 (log.f64 (/.f64 k (.f64 n (PI.f64)))) -1))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 n (/.f64 (PI.f64) k))) 1) 1))
(exp.f64 (-.f64 (*.f64 (log.f64 n) 1) (log.f64 (/.f64 k (PI.f64)))))
(exp.f64 (-.f64 (log.f64 n) (*.f64 (log.f64 (/.f64 k (PI.f64))) 1)))
(exp.f64 (-.f64 (.f64 (log.f64 n) 1) (.f64 (log.f64 (/.f64 k (PI.f64))) 1)))
(+.f64 0 (/.f64 k (PI.f64)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 k (PI.f64)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 k (PI.f64))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 k (PI.f64))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 k (PI.f64))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 k (PI.f64)))) 1)
(*.f64 k (/.f64 1 (PI.f64)))
(*.f64 (/.f64 k (PI.f64)) 1)
(*.f64 1 (/.f64 k (PI.f64)))
(*.f64 (cbrt.f64 (/.f64 k (PI.f64))) (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) 2) (cbrt.f64 (/.f64 k (PI.f64))))
(.f64 (cbrt.f64 (.f64 k k)) (*.f64 (cbrt.f64 k) (/.f64 1 (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (/.f64 k (PI.f64))))
(.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) (/.f64 1 (PI.f64))))
(*.f64 (neg.f64 k) (/.f64 1 (neg.f64 (PI.f64))))
(*.f64 (/.f64 1 (PI.f64)) k)
(.f64 (/.f64 (cbrt.f64 (.f64 k k)) 1) (/.f64 (cbrt.f64 k) (PI.f64)))
(*.f64 (/.f64 (sqrt.f64 k) 1) (/.f64 (sqrt.f64 k) (PI.f64)))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) -2) (/.f64 k (cbrt.f64 (PI.f64))))
(.f64 (/.f64 (cbrt.f64 (.f64 k k)) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (/.f64 k (PI.f64))))
(*.f64 (/.f64 (sqrt.f64 k) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (/.f64 (sqrt.f64 k) (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) -1/2) (/.f64 k (sqrt.f64 (PI.f64))))
(.f64 (/.f64 (cbrt.f64 (.f64 k k)) (sqrt.f64 (PI.f64))) (/.f64 (cbrt.f64 k) (sqrt.f64 (PI.f64))))
(pow.f64 (/.f64 k (PI.f64)) 1)
(pow.f64 (pow.f64 (/.f64 k (PI.f64)) 2) 1/2)
(pow.f64 (pow.f64 (/.f64 k (PI.f64)) 3) 1/3)
(pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) 3)
(pow.f64 (sqrt.f64 (/.f64 k (PI.f64))) 2)
(pow.f64 (/.f64 (PI.f64) k) -1)
(pow.f64 (exp.f64 1) (log.f64 (/.f64 k (PI.f64))))
(pow.f64 (/.f64 (pow.f64 k 3) (pow.f64 (PI.f64) 3)) 1/3)
(pow.f64 (/.f64 (/.f64 (PI.f64) k) 1) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 k (PI.f64)))) 2)) (cbrt.f64 (log.f64 (/.f64 k (PI.f64)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 k (PI.f64))))) (sqrt.f64 (log.f64 (/.f64 k (PI.f64)))))
(neg.f64 (/.f64 k (neg.f64 (PI.f64))))
(sqrt.f64 (pow.f64 (/.f64 k (PI.f64)) 2))
(log.f64 (exp.f64 (/.f64 k (PI.f64))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 k (PI.f64)))))
(cbrt.f64 (pow.f64 (/.f64 k (PI.f64)) 3))
(cbrt.f64 (/.f64 (pow.f64 k 3) (pow.f64 (PI.f64) 3)))
(expm1.f64 (log1p.f64 (/.f64 k (PI.f64))))
(log1p.f64 (expm1.f64 (/.f64 k (PI.f64))))
(exp.f64 (log.f64 (/.f64 k (PI.f64))))
(exp.f64 (*.f64 (log.f64 (/.f64 k (PI.f64))) 1))
(exp.f64 (.f64 (.f64 3 (log.f64 (/.f64 k (PI.f64)))) 1/3))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 k (PI.f64)))) 3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 k (PI.f64)))) 2))
(exp.f64 (*.f64 (log.f64 (/.f64 (PI.f64) k)) -1))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 k (PI.f64))) 1) 1))
(exp.f64 (-.f64 (*.f64 (log.f64 k) 1) (log.f64 (PI.f64))))
(exp.f64 (-.f64 (log.f64 k) (*.f64 (log.f64 (PI.f64)) 1)))
(exp.f64 (-.f64 (.f64 (log.f64 k) 1) (.f64 (log.f64 (PI.f64)) 1)))

Outputs
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
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(/.f64 (*.f64 n (PI.f64)) k)
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(/.f64 (*.f64 n (PI.f64)) k)
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(/.f64 (*.f64 n (PI.f64)) k)
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(+.f64 0 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k))))
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(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (*.f64 n (/.f64 (PI.f64) k))))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 n (*.f64 2 (/.f64 (PI.f64) k))))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k))))) 1)
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(pow.f64 (pow.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)) 3) 1/6)
(pow.f64 (pow.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) k))) 3) 1/6)
(pow.f64 (.f64 8 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 3)) 1/6)
(pow.f64 (pow.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)) 3/2) 1/3)
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(pow.f64 (cbrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) k)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(pow.f64 (pow.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)) 1/6) 3)
(sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(pow.f64 (pow.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)) 1/4) 2)
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(pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (.f64 (.f64 2 n) (/.f64 (PI.f64) k)))))
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(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) k))))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) k)))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))))))
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(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (neg.f64 n) (/.f64 1 (/.f64 (neg.f64 k) (PI.f64))))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (PI.f64) k) n)
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 n) 2) 1) (/.f64 (cbrt.f64 n) (/.f64 k (PI.f64))))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (sqrt.f64 n) 1) (/.f64 (sqrt.f64 n) (/.f64 k (PI.f64))))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (sqrt.f64 n) k) (/.f64 (sqrt.f64 n) (/.f64 1 (PI.f64))))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 1 k) (/.f64 n (/.f64 1 (PI.f64))))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 n) 2) k) (/.f64 (cbrt.f64 n) (/.f64 1 (PI.f64))))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) -2) (/.f64 n (cbrt.f64 (/.f64 k (PI.f64)))))
(/.f64 (*.f64 (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) -2) n) (cbrt.f64 (/.f64 k (PI.f64))))
(/.f64 (*.f64 n (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) -2)) (cbrt.f64 (/.f64 k (PI.f64))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 n) 2) (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) 2)) (cbrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(.f64 (cbrt.f64 (.f64 n (/.f64 (PI.f64) k))) (/.f64 (pow.f64 (cbrt.f64 n) 2) (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) 2)))
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) 2)) (/.f64 (sqrt.f64 n) (cbrt.f64 (/.f64 k (PI.f64)))))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (pow.f64 (/.f64 k (PI.f64)) -1/2) (/.f64 n (sqrt.f64 (/.f64 k (PI.f64)))))
(/.f64 (pow.f64 (/.f64 k (PI.f64)) -1/2) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) n))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 n) 2) (sqrt.f64 (/.f64 k (PI.f64)))) (/.f64 (cbrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 n 1) (/.f64 (PI.f64) k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 n (neg.f64 k)) (neg.f64 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (.f64 (/.f64 n k) 1) (PI.f64))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (.f64 (/.f64 n k) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) 1)
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) 2) 1/2)
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (pow.f64 (/.f64 k (*.f64 n (PI.f64))) -3) 1/3)
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) 3)
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) 2)
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (/.f64 k (*.f64 n (PI.f64))) -1)
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (exp.f64 1) (log.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (/.f64 (pow.f64 n 3) (pow.f64 (/.f64 k (PI.f64)) 3)) 1/3)
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (/.f64 (/.f64 k (*.f64 n (PI.f64))) 1) -1)
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 n (/.f64 (PI.f64) k)))) 2)) (cbrt.f64 (log.f64 (.f64 n (/.f64 (PI.f64) k)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 n (/.f64 (PI.f64) k))))) (sqrt.f64 (log.f64 (.f64 n (/.f64 (PI.f64) k)))))
(neg.f64 (/.f64 n (/.f64 (neg.f64 k) (PI.f64))))
(*.f64 n (/.f64 (PI.f64) k))
(sqrt.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) 2))
(*.f64 n (/.f64 (PI.f64) k))
(log.f64 (pow.f64 (exp.f64 n) (/.f64 (PI.f64) k)))
(*.f64 n (/.f64 (PI.f64) k))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(*.f64 n (/.f64 (PI.f64) k))
(cbrt.f64 (pow.f64 (/.f64 k (*.f64 n (PI.f64))) -3))
(*.f64 n (/.f64 (PI.f64) k))
(cbrt.f64 (/.f64 (pow.f64 n 3) (pow.f64 (/.f64 k (PI.f64)) 3)))
(*.f64 n (/.f64 (PI.f64) k))
(expm1.f64 (log1p.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 n (/.f64 (PI.f64) k))
(log1p.f64 (expm1.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (log.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (log.f64 (.f64 n (/.f64 (PI.f64) k))) 1))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (log.f64 (pow.f64 (/.f64 k (.f64 n (PI.f64))) -3)) 1/3))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 n (/.f64 (PI.f64) k)))) 3))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k)))) 2))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (log.f64 (/.f64 k (.f64 n (PI.f64)))) -1))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 n (/.f64 (PI.f64) k))) 1) 1))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (-.f64 (*.f64 (log.f64 n) 1) (log.f64 (/.f64 k (PI.f64)))))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (-.f64 (log.f64 n) (*.f64 (log.f64 (/.f64 k (PI.f64))) 1)))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (-.f64 (.f64 (log.f64 n) 1) (.f64 (log.f64 (/.f64 k (PI.f64))) 1)))
(*.f64 n (/.f64 (PI.f64) k))
(+.f64 0 (/.f64 k (PI.f64)))
(/.f64 k (PI.f64))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 k (PI.f64)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 k (PI.f64))))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (exp.f64 (/.f64 k (PI.f64)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 k (PI.f64))))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (/.f64 k (PI.f64))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 k (PI.f64))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 k (PI.f64))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (/.f64 k (PI.f64))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 k (PI.f64)))) 1)
(/.f64 k (PI.f64))
(*.f64 k (/.f64 1 (PI.f64)))
(/.f64 k (PI.f64))
(*.f64 (/.f64 k (PI.f64)) 1)
(/.f64 k (PI.f64))
(*.f64 1 (/.f64 k (PI.f64)))
(/.f64 k (PI.f64))
(*.f64 (cbrt.f64 (/.f64 k (PI.f64))) (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) 2))
(/.f64 k (PI.f64))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) 2) (cbrt.f64 (/.f64 k (PI.f64))))
(/.f64 k (PI.f64))
(.f64 (cbrt.f64 (.f64 k k)) (*.f64 (cbrt.f64 k) (/.f64 1 (PI.f64))))
(.f64 (cbrt.f64 (.f64 k k)) (*.f64 (/.f64 1 (PI.f64)) (cbrt.f64 k)))
(.f64 (cbrt.f64 (.f64 k k)) (/.f64 (cbrt.f64 k) (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 k (PI.f64))
(.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) (/.f64 1 (PI.f64))))
(/.f64 k (PI.f64))
(*.f64 (neg.f64 k) (/.f64 1 (neg.f64 (PI.f64))))
(/.f64 k (PI.f64))
(*.f64 (/.f64 1 (PI.f64)) k)
(/.f64 k (PI.f64))
(.f64 (/.f64 (cbrt.f64 (.f64 k k)) 1) (/.f64 (cbrt.f64 k) (PI.f64)))
(.f64 (cbrt.f64 (.f64 k k)) (*.f64 (/.f64 1 (PI.f64)) (cbrt.f64 k)))
(.f64 (cbrt.f64 (.f64 k k)) (/.f64 (cbrt.f64 k) (PI.f64)))
(*.f64 (/.f64 (sqrt.f64 k) 1) (/.f64 (sqrt.f64 k) (PI.f64)))
(/.f64 k (PI.f64))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) -2) (/.f64 k (cbrt.f64 (PI.f64))))
(.f64 (/.f64 (cbrt.f64 (.f64 k k)) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (/.f64 k (PI.f64))))
(.f64 (cbrt.f64 (/.f64 k (PI.f64))) (/.f64 (cbrt.f64 (.f64 k k)) (pow.f64 (cbrt.f64 (PI.f64)) 2)))
(/.f64 (cbrt.f64 (*.f64 k k)) (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (cbrt.f64 (/.f64 k (PI.f64)))))
(*.f64 (/.f64 (sqrt.f64 k) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (/.f64 (sqrt.f64 k) (cbrt.f64 (PI.f64))))
(/.f64 k (PI.f64))
(*.f64 (pow.f64 (PI.f64) -1/2) (/.f64 k (sqrt.f64 (PI.f64))))
(/.f64 (*.f64 (pow.f64 (PI.f64) -1/2) k) (sqrt.f64 (PI.f64)))
(/.f64 (pow.f64 (PI.f64) -1/2) (/.f64 (sqrt.f64 (PI.f64)) k))
(*.f64 (/.f64 (pow.f64 (PI.f64) -1/2) (sqrt.f64 (PI.f64))) k)
(.f64 (/.f64 (cbrt.f64 (.f64 k k)) (sqrt.f64 (PI.f64))) (/.f64 (cbrt.f64 k) (sqrt.f64 (PI.f64))))
(.f64 (cbrt.f64 (.f64 k k)) (*.f64 (/.f64 1 (PI.f64)) (cbrt.f64 k)))
(.f64 (cbrt.f64 (.f64 k k)) (/.f64 (cbrt.f64 k) (PI.f64)))
(pow.f64 (/.f64 k (PI.f64)) 1)
(/.f64 k (PI.f64))
(pow.f64 (pow.f64 (/.f64 k (PI.f64)) 2) 1/2)
(/.f64 k (PI.f64))
(pow.f64 (pow.f64 (/.f64 k (PI.f64)) 3) 1/3)
(/.f64 k (PI.f64))
(pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) 3)
(/.f64 k (PI.f64))
(pow.f64 (sqrt.f64 (/.f64 k (PI.f64))) 2)
(/.f64 k (PI.f64))
(pow.f64 (/.f64 (PI.f64) k) -1)
(/.f64 k (PI.f64))
(pow.f64 (exp.f64 1) (log.f64 (/.f64 k (PI.f64))))
(/.f64 k (PI.f64))
(pow.f64 (/.f64 (pow.f64 k 3) (pow.f64 (PI.f64) 3)) 1/3)
(/.f64 k (PI.f64))
(pow.f64 (/.f64 (/.f64 (PI.f64) k) 1) -1)
(/.f64 k (PI.f64))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 k (PI.f64)))) 2)) (cbrt.f64 (log.f64 (/.f64 k (PI.f64)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 k (PI.f64))))) (sqrt.f64 (log.f64 (/.f64 k (PI.f64)))))
(neg.f64 (/.f64 k (neg.f64 (PI.f64))))
(/.f64 k (PI.f64))
(sqrt.f64 (pow.f64 (/.f64 k (PI.f64)) 2))
(/.f64 k (PI.f64))
(log.f64 (exp.f64 (/.f64 k (PI.f64))))
(/.f64 k (PI.f64))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 k (PI.f64)))))
(/.f64 k (PI.f64))
(cbrt.f64 (pow.f64 (/.f64 k (PI.f64)) 3))
(/.f64 k (PI.f64))
(cbrt.f64 (/.f64 (pow.f64 k 3) (pow.f64 (PI.f64) 3)))
(/.f64 k (PI.f64))
(expm1.f64 (log1p.f64 (/.f64 k (PI.f64))))
(/.f64 k (PI.f64))
(log1p.f64 (expm1.f64 (/.f64 k (PI.f64))))
(/.f64 k (PI.f64))
(exp.f64 (log.f64 (/.f64 k (PI.f64))))
(/.f64 k (PI.f64))
(exp.f64 (*.f64 (log.f64 (/.f64 k (PI.f64))) 1))
(/.f64 k (PI.f64))
(exp.f64 (.f64 (.f64 3 (log.f64 (/.f64 k (PI.f64)))) 1/3))
(/.f64 k (PI.f64))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 k (PI.f64)))) 3))
(/.f64 k (PI.f64))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 k (PI.f64)))) 2))
(/.f64 k (PI.f64))
(exp.f64 (*.f64 (log.f64 (/.f64 (PI.f64) k)) -1))
(/.f64 k (PI.f64))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 k (PI.f64))) 1) 1))
(/.f64 k (PI.f64))
(exp.f64 (-.f64 (*.f64 (log.f64 k) 1) (log.f64 (PI.f64))))
(/.f64 k (PI.f64))
(exp.f64 (-.f64 (log.f64 k) (*.f64 (log.f64 (PI.f64)) 1)))
(/.f64 k (PI.f64))
(exp.f64 (-.f64 (.f64 (log.f64 k) 1) (.f64 (log.f64 (PI.f64)) 1)))
(/.f64 k (PI.f64))

localize14.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 k n) (*.f64 2 (PI.f64)))
✓	0.2b	(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64)))))
✓	9.7b	(sqrt.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64))))

Compiler

Compiled 38 to 21 computations (44.7% saved)

series6.3s (7.4%)

Counts

3 → 24

Calls

18 calls:

Time	Variable		Point	Expression
685.0ms	n	@	-inf	(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64)))))
681.0ms	k	@	inf	(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64)))))
675.0ms	n	@	inf	(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64)))))
674.0ms	k	@	-inf	(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64)))))
667.0ms	n	@	0	(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64)))))

Compiler

Compiled 776432 to 489152 computations (37% saved)

rewrite65.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

592×	`log-prod_binary64`
375×	`pow-prod-down_binary64`
285×	`pow2_binary64`
200×	`pow1/3_binary64`
199×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	40
1	234	37
2	3152	37

Stop Event

1×	node limit

Counts

3 → 165

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64)))))
(/.f64 (/.f64 k n) (*.f64 2 (PI.f64)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) (pow.f64 (*.f64 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(#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (/.f64 k n) 3) (pow.f64 (*.f64 2 (PI.f64)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) 1) 2))))))

simplify77.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

551×	`fma-def_binary64`
537×	`unswap-sqr_binary64`
512×	`times-frac_binary64`
506×	`distribute-rgt-in_binary64`
291×	`log-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	363	2731
1	832	2652
2	2607	2640

Stop Event

1×	node limit

Counts

189 → 248

Calls

Call 1

Inputs
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(+.f64 0 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))) 1)
(.f64 (sqrt.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) 1)
(.f64 1 (sqrt.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(.f64 (cbrt.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1/6))
(.f64 (pow.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1/6) (cbrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(.f64 (pow.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1/4) (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1/4))
(*.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (/.f64 1/2 (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) 1)
(/.f64 1 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))
(/.f64 1 (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 (/.f64 k n))))
(/.f64 (cbrt.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) (pow.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/6))
(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))
(/.f64 (pow.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1/4) (pow.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/4))
(/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (*.f64 2 (PI.f64))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) -1)
(/.f64 (sqrt.f64 (/.f64 (neg.f64 k) n)) (sqrt.f64 (*.f64 (PI.f64) -2)))
(/.f64 (sqrt.f64 (*.f64 (/.f64 k n) 1/2)) (sqrt.f64 (PI.f64)))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 k n))) (neg.f64 (sqrt.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1/2)
(pow.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) 1)
(pow.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) -1)
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -3/2) -1/3)
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 2) 1/4)
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 3) 1/6)
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/6) -3)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) 3/2)
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/4) -2)
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1/4) 2)
(pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) -1/2)
(pow.f64 (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 (/.f64 k n))) -1)
(fabs.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
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(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) 1))
(exp.f64 (.f64 (.f64 3/2 (log.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) 1/3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1/6)) 3))
(exp.f64 (.f64 (.f64 1/4 (log.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) 2))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) 1) 1/2))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) 1/2) 1))
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(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))) 1)
(.f64 1 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 1)
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(.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))))
(.f64 (pow.f64 (/.f64 k n) -1/2) (sqrt.f64 (.f64 2 (PI.f64))))
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(pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/2)
(pow.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) -1)
(pow.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 1)
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -3/2) 1/3)
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 2) -1/4)
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 3) -1/6)
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 3/2) -1/3)
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/6) 3)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) -3/2)
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1/6) -3)
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/4) 2)
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1/4) -2)
(pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/2)
(pow.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))) -1)
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
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(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) -1))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 1))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) -1/2))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -3/2)) 1/3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/6)) 3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/4)) 2))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) 1) -1/2))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) 1/2) -1))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) 1) -1))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) -1) 1))
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(.f64 (/.f64 (sqrt.f64 (/.f64 k n)) (pow.f64 (cbrt.f64 (.f64 2 (PI.f64))) 2)) (/.f64 (sqrt.f64 (/.f64 k n)) (cbrt.f64 (*.f64 2 (PI.f64)))))
(.f64 (/.f64 k (pow.f64 (cbrt.f64 (.f64 (PI.f64) 2)) 2)) (/.f64 1 (.f64 (cbrt.f64 (.f64 (PI.f64) 2)) n)))
(/.f64 (/.f64 k (.f64 n (cbrt.f64 (.f64 (PI.f64) 2)))) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) 2)) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) 2)) -2) (/.f64 k (.f64 n (cbrt.f64 (.f64 (PI.f64) 2)))))
(.f64 (/.f64 k (sqrt.f64 (.f64 2 (PI.f64)))) (/.f64 (/.f64 1 n) (sqrt.f64 (*.f64 2 (PI.f64)))))
(.f64 (/.f64 k (sqrt.f64 (.f64 (PI.f64) 2))) (/.f64 1 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) n)))
(/.f64 (/.f64 k (.f64 n (sqrt.f64 (.f64 (PI.f64) 2)))) (sqrt.f64 (*.f64 (PI.f64) 2)))
(/.f64 (/.f64 (/.f64 k n) (sqrt.f64 (.f64 (PI.f64) 2))) (sqrt.f64 (.f64 (PI.f64) 2)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 k n)) 2) (sqrt.f64 (.f64 2 (PI.f64)))) (/.f64 (cbrt.f64 (/.f64 k n)) (sqrt.f64 (*.f64 2 (PI.f64)))))
(.f64 (/.f64 k (sqrt.f64 (.f64 (PI.f64) 2))) (/.f64 1 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) n)))
(/.f64 (/.f64 k (.f64 n (sqrt.f64 (.f64 (PI.f64) 2)))) (sqrt.f64 (*.f64 (PI.f64) 2)))
(/.f64 (/.f64 (/.f64 k n) (sqrt.f64 (.f64 (PI.f64) 2))) (sqrt.f64 (.f64 (PI.f64) 2)))
(.f64 (pow.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 3/4) (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1/4))
(.f64 (pow.f64 (.f64 1/2 (/.f64 k (.f64 n (PI.f64)))) 1/4) (pow.f64 (.f64 1/2 (/.f64 k (*.f64 n (PI.f64)))) 3/4))
(.f64 (pow.f64 (.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n)) 1/4) (pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n)) 3/4))
(*.f64 (pow.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n))) 1/4) (pow.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n))) 3/4))
(.f64 (pow.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 5/6) (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1/6))
(.f64 (pow.f64 (.f64 1/2 (/.f64 k (.f64 n (PI.f64)))) 1/6) (pow.f64 (.f64 1/2 (/.f64 k (*.f64 n (PI.f64)))) 5/6))
(.f64 (pow.f64 (.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n)) 1/6) (pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n)) 5/6))
(*.f64 (pow.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n))) 1/6) (pow.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n))) 5/6))
(pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1)
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) 2)
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(pow.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) -2)
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 2) 1/2)
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 3) 1/3)
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 3/2) 2/3)
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(pow.f64 (cbrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) 3)
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1/6) 6)
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1/4) 4)
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) -1)
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(pow.f64 (/.f64 (pow.f64 (/.f64 k n) 3) (pow.f64 (*.f64 2 (PI.f64)) 3)) 1/3)
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(pow.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))) -1)
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(pow.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k) -1)
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(pow.f64 (/.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1) -1)
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(neg.f64 (/.f64 (/.f64 k n) (*.f64 (PI.f64) -2)))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(sqrt.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 2))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(log.f64 (pow.f64 (exp.f64 (/.f64 k n)) (/.f64 1/2 (PI.f64))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 3))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(cbrt.f64 (/.f64 (pow.f64 (/.f64 k n) 3) (pow.f64 (*.f64 2 (PI.f64)) 3)))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(exp.f64 (log.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) 1))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) 2))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(exp.f64 (.f64 (.f64 2 (log.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) 1/2))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) 1/3))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) 3))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(exp.f64 (.f64 (log.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) -1))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) 1) 1))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))) 1/2) 2))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) 1) 2))
(.f64 1/2 (/.f64 k (.f64 n (PI.f64))))
(*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n))
(/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))

localize18.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (PI.f64) (/.f64 k n))
✓	0.4b	(pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 3/2)
✓	10.3b	(cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))

Compiler

Compiled 40 to 17 computations (57.5% saved)

series6.1s (7.2%)

Counts

3 → 24

Calls

18 calls:

Time	Variable		Point	Expression
840.0ms	k	@	inf	(pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 3/2)
811.0ms	n	@	inf	(pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 3/2)
795.0ms	n	@	0	(pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 3/2)
773.0ms	k	@	0	(pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 3/2)
648.0ms	k	@	-inf	(pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 3/2)

Compiler

Compiled 618688 to 533648 computations (13.7% saved)

rewrite63.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

591×	`log-prod_binary64`
306×	`pow-prod-down_binary64`
291×	`pow2_binary64`
250×	`pow-unpow_binary64`
200×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	239	34
2	3115	34

Stop Event

1×	node limit

Counts

3 → 120

Calls

Call 1

Inputs
(cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 3/2)
(/.f64 (PI.f64) (/.f64 k n))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))) (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 2) (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))) (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 2)) (cbrt.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (cbrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1/6) (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (*.f64 2 (PI.f64))) (cbrt.f64 (/.f64 k n)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2)) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 2)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1/6)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 2))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 1) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 1/3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))) 1) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1/6) (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1/4) (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 (/.f64 k n)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2/3 (log.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1/4)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 1/3) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))) 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))) 3/4) 2))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (PI.f64) (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 n k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (PI.f64) (/.f64 n k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 n (/.f64 (PI.f64) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (PI.f64) (/.f64 n k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (PI.f64) (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (*.f64 (cbrt.f64 (PI.f64)) (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 2) (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 n k) (PI.f64))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) k) n)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) 1) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 k n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (PI.f64)) 1) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 k n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) k) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 1 n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 k n)) -2) (/.f64 (PI.f64) (cbrt.f64 (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (cbrt.f64 (pow.f64 (/.f64 n k) -2))) (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (pow.f64 (/.f64 n k) -2))) (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 k n) -1/2) (/.f64 (PI.f64) (sqrt.f64 (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (sqrt.f64 (/.f64 k n))) (/.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) 1) (/.f64 n k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) (neg.f64 k)) (neg.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (PI.f64) k) 1) n)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (PI.f64) k) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (PI.f64) k) (sqrt.f64 n)) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 k n) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (PI.f64) (/.f64 (neg.f64 k) n)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 k n) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 k (*.f64 (PI.f64) n))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))) 1) 1))))))

simplify74.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

639×	`associate-*r/_binary64`
400×	`associate-/l*_binary64`
351×	`fma-def_binary64`
259×	`distribute-rgt-in_binary64`
254×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	291	1772
1	634	1695
2	1808	1695
3	7979	1695

Stop Event

1×	node limit

Counts

144 → 161

Calls

Call 1

Inputs
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(+.f64 0 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))))) (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))))))
(-.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))))) 1)
(.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 1)
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(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))) 2)) (cbrt.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))) (cbrt.f64 2))
(.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/6) (pow.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1/6))
(/.f64 (cbrt.f64 (*.f64 2 (PI.f64))) (cbrt.f64 (/.f64 k n)))
(pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/3)
(pow.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))) 1)
(pow.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))) 2/3)
(pow.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 2)) 1/6)
(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 3) 1/9)
(pow.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))) 2) 1/2)
(pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))) 3)
(pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))) 2)) 3/2)
(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/6) 2)
(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))) 2))
(log.f64 (exp.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))))
(log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))))))
(expm1.f64 (log1p.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))))
(log1p.f64 (expm1.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))))
(exp.f64 (log.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 1/3))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))) 1))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))) 3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1/6)) 2))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 2))) 3/2))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))) 1) 1/3))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))) 1/3) 1))
(exp.f64 (.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))) 1) 1))
(+.f64 0 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))))) 1)
(.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))) (pow.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1/6))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 1)
(.f64 1 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))))
(.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/6) (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
(.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/4) (pow.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1/4))
(/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 (/.f64 k n)))
(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))
(fabs.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))))))
(cbrt.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))) 1))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 1/2))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2)) 1/3))
(exp.f64 (.f64 (.f64 2/3 (log.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))) 3/4))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1/6)) 3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1/4)) 2))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))) 1) 1/2))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))) 1/3) 3/2))
(exp.f64 (.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))) 1) 3/2))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))) 1) 1))
(exp.f64 (.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))) 3/4) 2))
(+.f64 0 (*.f64 (PI.f64) (/.f64 n k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 n k)))) 1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (.f64 (PI.f64) (/.f64 n k)) 1)
(.f64 1 (.f64 (PI.f64) (/.f64 n k)))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) (/.f64 n k)))
(.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))) 2) (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (/.f64 n k)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 (/.f64 (PI.f64) k) n)
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) 1) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 k n)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) 1) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 k n)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 n)))
(*.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) k) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 1 n)))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 k n)) -2) (/.f64 (PI.f64) (cbrt.f64 (/.f64 k n))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (cbrt.f64 (pow.f64 (/.f64 n k) -2))) (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (pow.f64 (/.f64 n k) -2))) (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (/.f64 k n))))
(*.f64 (pow.f64 (/.f64 k n) -1/2) (/.f64 (PI.f64) (sqrt.f64 (/.f64 k n))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (sqrt.f64 (/.f64 k n))) (/.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (/.f64 k n))))
(*.f64 (/.f64 (PI.f64) 1) (/.f64 n k))
(*.f64 (/.f64 (PI.f64) (neg.f64 k)) (neg.f64 n))
(.f64 (.f64 (/.f64 (PI.f64) k) 1) n)
(.f64 (.f64 (/.f64 (PI.f64) k) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n))
(.f64 (.f64 (/.f64 (PI.f64) k) (sqrt.f64 n)) (sqrt.f64 n))
(pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 1)
(pow.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2) 1/2)
(pow.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -3) 1/3)
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 3)
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 2)
(pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -1)
(pow.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 k n) 3)) 1/3)
(pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) 1) -1)
(neg.f64 (/.f64 (PI.f64) (/.f64 (neg.f64 k) n)))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k)))))
(cbrt.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -3))
(cbrt.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 k n) 3)))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 n k))))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k))))
(exp.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k))) 1))
(exp.f64 (.f64 (log.f64 (pow.f64 (/.f64 k (.f64 (PI.f64) n)) -3)) 1/3))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k)))) 3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k)))) 2))
(exp.f64 (.f64 (log.f64 (/.f64 k (.f64 (PI.f64) n))) -1))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))) 1) 1))

Outputs
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(+.f64 0 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))))
(cbrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))
(cbrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))))
(.f64 (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))) 3)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))))) (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (.f64 (*.f64 (PI.f64) (/.f64 n k)) 2))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))))
(-.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))))) 1)
(cbrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))
(cbrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 1)
(cbrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))
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(.f64 1 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))
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(cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(.f64 (cbrt.f64 2) (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))))
(.f64 (cbrt.f64 2) (cbrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))) (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 2)))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))) (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 (*.f64 (PI.f64) (/.f64 n k)) 2)) 2)))
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(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(+.f64 0 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 n k)))) 1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (PI.f64) (/.f64 n k))
(.f64 (.f64 (PI.f64) (/.f64 n k)) 1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 1 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 2))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))) 2) (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (PI.f64) k) n)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) 1) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 k n)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) 1) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 k n)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 n)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) k) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 1 n)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 k n)) -2) (/.f64 (PI.f64) (cbrt.f64 (/.f64 k n))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (cbrt.f64 (pow.f64 (/.f64 n k) -2))) (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))) (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (cbrt.f64 (pow.f64 (/.f64 n k) -2))))
(.f64 (cbrt.f64 (.f64 n (/.f64 (PI.f64) k))) (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (cbrt.f64 (pow.f64 (/.f64 n k) -2))))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (pow.f64 (/.f64 n k) -2))) (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (/.f64 k n))))
(/.f64 (/.f64 (PI.f64) (cbrt.f64 (/.f64 k n))) (cbrt.f64 (pow.f64 (/.f64 n k) -2)))
(/.f64 (PI.f64) (*.f64 (cbrt.f64 (/.f64 k n)) (cbrt.f64 (pow.f64 (/.f64 n k) -2))))
(*.f64 (pow.f64 (/.f64 k n) -1/2) (/.f64 (PI.f64) (sqrt.f64 (/.f64 k n))))
(*.f64 (/.f64 (pow.f64 (/.f64 k n) -1/2) (sqrt.f64 (/.f64 k n))) (PI.f64))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (sqrt.f64 (/.f64 k n))) (/.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (/.f64 k n))))
(/.f64 (/.f64 (PI.f64) (sqrt.f64 (/.f64 k n))) (sqrt.f64 (/.f64 k n)))
(/.f64 (PI.f64) (*.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (/.f64 k n))))
(*.f64 (/.f64 (PI.f64) 1) (/.f64 n k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (PI.f64) (neg.f64 k)) (neg.f64 n))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (.f64 (/.f64 (PI.f64) k) 1) n)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (.f64 (/.f64 (PI.f64) k) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (.f64 (/.f64 (PI.f64) k) (sqrt.f64 n)) (sqrt.f64 n))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2) 1/2)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -3) 1/3)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 3)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 2)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 k n) 3)) 1/3)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) 1) -1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(neg.f64 (/.f64 (PI.f64) (/.f64 (neg.f64 k) n)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k)))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(cbrt.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -3))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(cbrt.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 k n) 3)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k))) 1))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (log.f64 (pow.f64 (/.f64 k (.f64 (PI.f64) n)) -3)) 1/3))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k)))) 3))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k)))) 2))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (log.f64 (/.f64 k (.f64 (PI.f64) n))) -1))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))) 1) 1))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))

localize34.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	0.2b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
✓	9.7b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))

Compiler

Compiled 80 to 55 computations (31.3% saved)

series6.2s (7.3%)

Counts

3 → 36

Calls

18 calls:

Time	Variable		Point	Expression
1.3s	k	@	0	(/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
1.2s	k	@	-inf	(/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
1.1s	k	@	inf	(/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
695.0ms	k	@	-inf	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
685.0ms	k	@	0	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))

Compiler

Compiled 777928 to 540752 computations (30.5% saved)

rewrite69.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

713×	`log-prod_binary64`
483×	`pow-unpow_binary64`
359×	`pow2_binary64`
244×	`pow1/3_binary64`
241×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	55
1	285	52
2	3752	52

Stop Event

1×	node limit

Counts

3 → 102

Calls

Call 1

Inputs

(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))

(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))

(/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))

Outputs

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simplify67.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

641×	`fma-def_binary64`
573×	`times-frac_binary64`
351×	`distribute-rgt-in_binary64`
347×	`unswap-sqr_binary64`
346×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	279	3532
1	631	2959
2	2254	2946

Stop Event

1×	node limit

Counts

138 → 182

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(.f64 2 (.f64 n (PI.f64)))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 2 (.f64 n (PI.f64))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 n (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 -1 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2) (PI.f64)))) (.f64 2 (.f64 n (PI.f64)))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 1/3 (.f64 n (.f64 (pow.f64 (.f64 -1 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 3) (.f64 (pow.f64 k 3) (PI.f64))))) (+.f64 (.f64 n (.f64 (pow.f64 k 2) (.f64 (pow.f64 (.f64 -1 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2) (PI.f64)))) (.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(/.f64 1 (sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)))
(/.f64 1 (sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)))
(/.f64 1 (sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)))
(/.f64 1 (sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)))
(/.f64 1 (sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)))
(/.f64 1 (sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)))
(/.f64 1 (sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)))
(/.f64 1 (sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)))
(+.f64 0 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 1)
(.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1)
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4) (pow.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 (pow.f64 k -1)))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 1 (sqrt.f64 k)))
(.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 2))) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(/.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1)
(/.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))
(/.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4) (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) -1)
(/.f64 (sqrt.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/2)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1)
(pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) -1)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4) 2)
(pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) -1)
(fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 1))
(+.f64 0 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) 1)
(.f64 (.f64 2 (.f64 (PI.f64) n)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (neg.f64 k)))
(.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 1 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k)))
(.f64 (.f64 2 (.f64 (PI.f64) n)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (neg.f64 k) 1)))
(.f64 1 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))
(.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1)
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (-.f64 1 k)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (-.f64 1 k)))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
(.f64 (/.f64 n (pow.f64 n k)) (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (/.f64 n (pow.f64 n k)))
(.f64 (pow.f64 1 (-.f64 1 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 2)) (-.f64 1 k)) (pow.f64 (cbrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)))
(.f64 (pow.f64 (.f64 n 2) (-.f64 1 k)) (pow.f64 (PI.f64) (-.f64 1 k)))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (neg.f64 k)) (.f64 2 (*.f64 (PI.f64) n)))
(/.f64 n (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (*.f64 2 (PI.f64))))
(/.f64 (.f64 2 (PI.f64)) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) n))
(/.f64 (.f64 2 (.f64 (PI.f64) n)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k))
(/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (.f64 2 (.f64 (PI.f64) n))))
(/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 2)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (cbrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(/.f64 (.f64 n 2) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) (PI.f64)))
(/.f64 (neg.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 2 (-.f64 1 k))))
(log.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) 3))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
(exp.f64 (log.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 1))
(+.f64 0 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))) 1)
(.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) 1)
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))) (cbrt.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))
(.f64 (cbrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))
(.f64 (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))) (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))
(.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))
(.f64 (/.f64 1 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (sqrt.f64 k))
(.f64 (/.f64 1 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) -1/2)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) -1)
(pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) 1)
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) 3) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))) 2)
(pow.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 1/2)
(pow.f64 (neg.f64 (neg.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))) -1)
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) 3))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) -1))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) 1))

Outputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
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(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))) 1)
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) 1)
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))) (cbrt.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))) (cbrt.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))) (cbrt.f64 (/.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))
(.f64 (cbrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))) (cbrt.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))) (cbrt.f64 (/.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))
(.f64 (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))) (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))
(/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)))
(/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(.f64 (/.f64 1 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (sqrt.f64 k))
(/.f64 (.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(.f64 (/.f64 1 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))) (/.f64 1 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))))
(/.f64 (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) -1/2)
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k) -1/2)
(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) -1/2)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) -1)
(/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)))
(/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) 1)
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) 3) 1/3)
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))) 3)
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))) 2)
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(pow.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 1/2)
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(pow.f64 (neg.f64 (neg.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))) -1)
(/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)))
(/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) 3))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) -1))
(/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)))
(/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) 1))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))

eval411.0ms (0.5%)

Compiler: Compiled 18823 to 12676 computations (32.7% saved)

prune555.0ms (0.7%)

Pruning

40 alts after pruning (33 fresh and 7 done)

	Pruned	Kept	Total
New	979	18	997
Fresh	9	15	24
Picked	0	1	1
Done	2	6	8
Total	990	40	1030

Error

Counts

1030 → 40

Alt Table

Click to see full alt table

Status	Error	Program
	35.2b	(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/6) 3)
	35.2b	(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/3) 3/2)
	35.1b	(pow.f64 (pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n)) 1/6) -3)
	35.1b	(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/6) 3)
	10.5b	(pow.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))) -1/2)
	32.7b	(pow.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n))) -1/2)
	32.7b	(pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/2)
	32.9b	(pow.f64 (cbrt.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))) -3/2)
	33.1b	(pow.f64 (cbrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k))) 3/2)
✓	0.4b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
✓	0.4b	(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
	0.5b	(/.f64 (pow.f64 k -1/2) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (neg.f64 (-.f64 1 k))))
✓	22.6b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
	22.7b	(/.f64 (sqrt.f64 (*.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64))))
	32.8b	(/.f64 1 (pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1/4) 2))
	32.8b	(/.f64 1 (pow.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))) -1/2))
	0.4b	(/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)) (pow.f64 k -1/2)))
✓	10.6b	(/.f64 1 (/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))))
	10.4b	(/.f64 1 (/.f64 1 (sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (/.f64 n (pow.f64 n k))) k))))
✓	32.7b	(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64)))))
	32.7b	(/.f64 1 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))))
	22.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
	32.9b	(.f64 (sqrt.f64 (.f64 n (/.f64 2 k))) (sqrt.f64 (PI.f64)))
	33.0b	(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 (/.f64 n k)))
	22.9b	(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 2 (/.f64 k (PI.f64)))))
	0.5b	(.f64 (neg.f64 (pow.f64 k -1/2)) (/.f64 1 (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/2)))))
	10.6b	(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))
	32.8b	(sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k))
	10.4b	(sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k))
	32.8b	(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))))
	32.8b	(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
	10.4b	(sqrt.f64 (/.f64 2 (/.f64 k (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) k)))))
	32.8b	(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))
	32.8b	(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)))
	33.0b	(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))))
	12.9b	(sqrt.f64 (.f64 n (-.f64 (+.f64 1 (.f64 (/.f64 2 k) (PI.f64))) 1)))
✓	32.8b	(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
	32.8b	(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 n (/.f64 1 (PI.f64))))))
✓	34.7b	(exp.f64 (.f64 (log.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))) 1/2))
	38.4b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -3/2))

Compiler

Compiled 536 to 439 computations (18.1% saved)

regimes236.0ms (0.3%)

Counts

91 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)))
(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k))
(pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/2)
(pow.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64)))) -1/2)
(pow.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n))) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 2 n)))))
(/.f64 1 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 2 n))))
(/.f64 1 (pow.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))) -1/2))
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 n (/.f64 1 (PI.f64))))))
(sqrt.f64 (.f64 n (-.f64 (+.f64 1 (.f64 (/.f64 2 k) (PI.f64))) 1)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 2 (/.f64 k (PI.f64)))))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 (/.f64 n k)))
(.f64 (sqrt.f64 (.f64 n (/.f64 2 k))) (sqrt.f64 (PI.f64)))
(/.f64 (sqrt.f64 (*.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)) 3/2))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -3/2))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))))
(pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))) -3/2)
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))) 1/2))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))))
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n)) 1/6) -3)
(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/3) 3/2)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/6) 3)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/4) 2)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2) 1/3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))
(/.f64 1 (pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1/4) 2))
(pow.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))) -1/2)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 1 (/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))))
(/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)) (pow.f64 k -1/2)))
(.f64 (neg.f64 (pow.f64 k -1/2)) (/.f64 1 (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/2)))))
(.f64 (pow.f64 k -1/2) (.f64 -1 (/.f64 1 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))))))
(.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 k)))
(/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 3/2) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(/.f64 (pow.f64 k -1/2) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (neg.f64 (-.f64 1 k))))
(/.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) -1/2))
(sqrt.f64 (/.f64 2 (/.f64 k (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) k)))))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k))
(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) -1/2)))
(pow.f64 (.f64 (/.f64 k 2) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k) (.f64 n (PI.f64)))) -1/2)
(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 1 (.f64 2 (*.f64 k -1/2)))))
(/.f64 1 (/.f64 1 (sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (/.f64 n (pow.f64 n k))) k))))
(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 2 (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (*.f64 k 1/2)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)))
(/.f64 (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 1 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))))) 2))
(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n 2) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k) (PI.f64))))))
(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 n 2) (PI.f64))) (pow.f64 (.f64 (.f64 n 2) (PI.f64)) (.f64 k -1/2))) (sqrt.f64 k))
(.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 k -1/2)) (pow.f64 k -1/2)))
(/.f64 (/.f64 1 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 1/2 k)) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k 1/4)))
(/.f64 (+.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))) (sqrt.f64 k))

Outputs
(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 n 2) (PI.f64))) (pow.f64 (.f64 (.f64 n 2) (PI.f64)) (.f64 k -1/2))) (sqrt.f64 k))

Calls

5 calls:

48.0ms	n
43.0ms	(.f64 (.f64 2 (PI.f64)) n)
42.0ms	k
41.0ms	(.f64 (.f64 2 (PI.f64)) n)
28.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.3b	1	`k`
0.3b	1	`n`
0.3b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.3b	1	`(.f64 (.f64 2 (PI.f64)) n)`
0.3b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 1261 to 853 computations (32.4% saved)

regimes209.0ms (0.2%)

Counts

86 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)))
(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k))
(pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/2)
(pow.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64)))) -1/2)
(pow.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n))) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 2 n)))))
(/.f64 1 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 2 n))))
(/.f64 1 (pow.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))) -1/2))
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 n (/.f64 1 (PI.f64))))))
(sqrt.f64 (.f64 n (-.f64 (+.f64 1 (.f64 (/.f64 2 k) (PI.f64))) 1)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 2 (/.f64 k (PI.f64)))))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 (/.f64 n k)))
(.f64 (sqrt.f64 (.f64 n (/.f64 2 k))) (sqrt.f64 (PI.f64)))
(/.f64 (sqrt.f64 (*.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)) 3/2))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -3/2))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))))
(pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))) -3/2)
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))) 1/2))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))))
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n)) 1/6) -3)
(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/3) 3/2)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/6) 3)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/4) 2)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2) 1/3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))
(/.f64 1 (pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1/4) 2))
(pow.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))) -1/2)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 1 (/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))))
(/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)) (pow.f64 k -1/2)))
(.f64 (neg.f64 (pow.f64 k -1/2)) (/.f64 1 (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/2)))))
(.f64 (pow.f64 k -1/2) (.f64 -1 (/.f64 1 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))))))
(.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 k)))
(/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 3/2) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(/.f64 (pow.f64 k -1/2) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (neg.f64 (-.f64 1 k))))
(/.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) -1/2))
(sqrt.f64 (/.f64 2 (/.f64 k (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) k)))))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k))
(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) -1/2)))
(pow.f64 (.f64 (/.f64 k 2) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k) (.f64 n (PI.f64)))) -1/2)
(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 1 (.f64 2 (*.f64 k -1/2)))))
(/.f64 1 (/.f64 1 (sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (/.f64 n (pow.f64 n k))) k))))
(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 2 (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (*.f64 k 1/2)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)))
(/.f64 (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 1 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))))) 2))
(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n 2) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k) (PI.f64))))))

Outputs
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n 2) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k) (PI.f64))))))

Calls

5 calls:

40.0ms	k
39.0ms	(.f64 (.f64 2 (PI.f64)) n)
39.0ms	(.f64 (.f64 2 (PI.f64)) n)
39.0ms	n
20.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.3b	1	`k`
0.3b	1	`n`
0.3b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.3b	1	`(.f64 (.f64 2 (PI.f64)) n)`
0.3b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 1150 to 781 computations (32.1% saved)

regimes210.0ms (0.2%)

Counts

85 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)))
(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k))
(pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/2)
(pow.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64)))) -1/2)
(pow.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n))) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 2 n)))))
(/.f64 1 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 2 n))))
(/.f64 1 (pow.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))) -1/2))
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 n (/.f64 1 (PI.f64))))))
(sqrt.f64 (.f64 n (-.f64 (+.f64 1 (.f64 (/.f64 2 k) (PI.f64))) 1)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 2 (/.f64 k (PI.f64)))))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 (/.f64 n k)))
(.f64 (sqrt.f64 (.f64 n (/.f64 2 k))) (sqrt.f64 (PI.f64)))
(/.f64 (sqrt.f64 (*.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)) 3/2))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -3/2))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))))
(pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))) -3/2)
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))) 1/2))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))))
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n)) 1/6) -3)
(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/3) 3/2)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/6) 3)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/4) 2)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2) 1/3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))
(/.f64 1 (pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1/4) 2))
(pow.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))) -1/2)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 1 (/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))))
(/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)) (pow.f64 k -1/2)))
(.f64 (neg.f64 (pow.f64 k -1/2)) (/.f64 1 (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/2)))))
(.f64 (pow.f64 k -1/2) (.f64 -1 (/.f64 1 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))))))
(.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 k)))
(/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 3/2) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(/.f64 (pow.f64 k -1/2) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (neg.f64 (-.f64 1 k))))
(/.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) -1/2))
(sqrt.f64 (/.f64 2 (/.f64 k (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) k)))))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) k))
(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) -1/2)))
(pow.f64 (.f64 (/.f64 k 2) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k) (.f64 n (PI.f64)))) -1/2)
(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 1 (.f64 2 (*.f64 k -1/2)))))
(/.f64 1 (/.f64 1 (sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (/.f64 n (pow.f64 n k))) k))))
(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 2 (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (*.f64 k 1/2)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)))
(/.f64 (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 1 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))))) 2))
(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Outputs
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))

Calls

5 calls:

40.0ms	k
39.0ms	n
39.0ms	(.f64 (.f64 2 (PI.f64)) n)
39.0ms	(.f64 (.f64 2 (PI.f64)) n)
20.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.4b	1	`k`
0.4b	1	`n`
0.4b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.4b	1	`(.f64 (.f64 2 (PI.f64)) n)`
0.4b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 1131 to 769 computations (32% saved)

regimes107.0ms (0.1%)

Counts

48 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)))
(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k))
(pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/2)
(pow.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64)))) -1/2)
(pow.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n))) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 2 n)))))
(/.f64 1 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 2 n))))
(/.f64 1 (pow.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))) -1/2))
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 n (/.f64 1 (PI.f64))))))
(sqrt.f64 (.f64 n (-.f64 (+.f64 1 (.f64 (/.f64 2 k) (PI.f64))) 1)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 2 (/.f64 k (PI.f64)))))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 (/.f64 n k)))
(.f64 (sqrt.f64 (.f64 n (/.f64 2 k))) (sqrt.f64 (PI.f64)))
(/.f64 (sqrt.f64 (*.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)) 3/2))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -3/2))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))))
(pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))) -3/2)
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))) 1/2))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))))
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n)) 1/6) -3)
(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/3) 3/2)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/6) 3)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/4) 2)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2) 1/3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))
(/.f64 1 (pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1/4) 2))
(pow.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))) -1/2)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Outputs
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))

Calls

4 calls:

24.0ms	(.f64 (.f64 2 (PI.f64)) n)
24.0ms	n
24.0ms	(.f64 (.f64 2 (PI.f64)) n)
21.0ms	k

Results

Error	Segments	Branch
0.4b	1	`k`
0.4b	1	`n`
0.4b	1	`(.f64 (.f64 2 (PI.f64)) n)`
0.4b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 508 to 334 computations (34.3% saved)

regimes177.0ms (0.2%)

Counts

46 → 2

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)))
(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k))
(pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/2)
(pow.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64)))) -1/2)
(pow.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n))) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 2 n)))))
(/.f64 1 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 2 n))))
(/.f64 1 (pow.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))) -1/2))
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 n (/.f64 1 (PI.f64))))))
(sqrt.f64 (.f64 n (-.f64 (+.f64 1 (.f64 (/.f64 2 k) (PI.f64))) 1)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 2 (/.f64 k (PI.f64)))))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 (/.f64 n k)))
(.f64 (sqrt.f64 (.f64 n (/.f64 2 k))) (sqrt.f64 (PI.f64)))
(/.f64 (sqrt.f64 (*.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)) 3/2))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -3/2))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))))
(pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))) -3/2)
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))) 1/2))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))))
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n)) 1/6) -3)
(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/3) 3/2)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/6) 3)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/4) 2)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2) 1/3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k)) k))
(/.f64 1 (pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) 1/4) 2))
(pow.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))) -1/2)

Outputs
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))

Calls

3 calls:

63.0ms	(.f64 (.f64 2 (PI.f64)) n)
60.0ms	n
41.0ms	k

Results

Error	Segments	Branch
0.4b	2	`k`
9.2b	3	`n`
9.2b	3	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 472 to 308 computations (34.7% saved)

bsearch19.0ms (0%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
19.0ms	8.229574691627475e-19	1.5540466285221788e-16

Results

17.0ms

112×

body

256

valid

Compiler

Compiled 212 to 173 computations (18.4% saved)

regimes225.0ms (0.3%)

Counts

42 → 2

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)))
(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k))
(pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/2)
(pow.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64)))) -1/2)
(pow.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n))) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 2 n)))))
(/.f64 1 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 2 n))))
(/.f64 1 (pow.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))) -1/2))
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 n (/.f64 1 (PI.f64))))))
(sqrt.f64 (.f64 n (-.f64 (+.f64 1 (.f64 (/.f64 2 k) (PI.f64))) 1)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 2 (/.f64 k (PI.f64)))))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 (/.f64 n k)))
(.f64 (sqrt.f64 (.f64 n (/.f64 2 k))) (sqrt.f64 (PI.f64)))
(/.f64 (sqrt.f64 (*.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)) 3/2))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -3/2))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))))
(pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))) -3/2)
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n))) 1/2))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))))
(pow.f64 (pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 1/2 n)) 1/6) -3)
(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/3) 3/2)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/6) 3)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/4) 2)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2) 1/3)

Outputs
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
(sqrt.f64 (.f64 n (-.f64 (+.f64 1 (.f64 (/.f64 2 k) (PI.f64))) 1)))

Calls

3 calls:

88.0ms	(.f64 (.f64 2 (PI.f64)) n)
87.0ms	n
36.0ms	k

Results

Error	Segments	Branch
2.6b	2	`k`
10.6b	5	`n`
10.6b	5	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 422 to 274 computations (35.1% saved)

bsearch13.0ms (0%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
13.0ms	1.0231225833862382e-19	3.053526616682645e-19

Results

12.0ms

80×

body

256

valid

Compiler

Compiled 158 to 134 computations (15.2% saved)

regimes142.0ms (0.2%)

Counts

24 → 2

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)))
(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k))
(pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/2)
(pow.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64)))) -1/2)
(pow.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n))) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 2 n)))))
(/.f64 1 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 2 n))))
(/.f64 1 (pow.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))) -1/2))
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 n (/.f64 1 (PI.f64))))))
(sqrt.f64 (.f64 n (-.f64 (+.f64 1 (.f64 (/.f64 2 k) (PI.f64))) 1)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 2 (/.f64 k (PI.f64)))))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 (/.f64 n k)))
(.f64 (sqrt.f64 (.f64 n (/.f64 2 k))) (sqrt.f64 (PI.f64)))
(/.f64 (sqrt.f64 (*.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64))))

Outputs
(/.f64 (sqrt.f64 (*.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64))))
(sqrt.f64 (.f64 n (-.f64 (+.f64 1 (.f64 (/.f64 2 k) (PI.f64))) 1)))

Calls

3 calls:

56.0ms	n
55.0ms	(.f64 (.f64 2 (PI.f64)) n)
24.0ms	k

Results

Error	Segments	Branch
2.6b	2	`k`
10.6b	5	`n`
10.6b	5	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 233 to 151 computations (35.2% saved)

bsearch14.0ms (0%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
13.0ms	1.0231225833862382e-19	3.053526616682645e-19

Results

12.0ms

80×

body

256

valid

Compiler

Compiled 158 to 134 computations (15.2% saved)

regimes139.0ms (0.2%)

Counts

23 → 2

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)))
(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k))
(pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/2)
(pow.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64)))) -1/2)
(pow.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n))) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 2 n)))))
(/.f64 1 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 2 n))))
(/.f64 1 (pow.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))) -1/2))
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 n (/.f64 1 (PI.f64))))))
(sqrt.f64 (.f64 n (-.f64 (+.f64 1 (.f64 (/.f64 2 k) (PI.f64))) 1)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 2 (/.f64 k (PI.f64)))))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 (/.f64 n k)))
(.f64 (sqrt.f64 (.f64 n (/.f64 2 k))) (sqrt.f64 (PI.f64)))

Outputs
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 2 (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 n (-.f64 (+.f64 1 (.f64 (/.f64 2 k) (PI.f64))) 1)))

Calls

3 calls:

55.0ms	n
54.0ms	(.f64 (.f64 2 (PI.f64)) n)
23.0ms	k

Results

Error	Segments	Branch
2.8b	2	`k`
10.6b	5	`n`
10.6b	5	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 224 to 146 computations (34.8% saved)

bsearch13.0ms (0%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
13.0ms	1.0231225833862382e-19	3.053526616682645e-19

Results

12.0ms

80×

body

256

valid

Compiler

Compiled 158 to 134 computations (15.2% saved)

regimes38.0ms (0%)

Counts

20 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)))
(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k))
(pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/2)
(pow.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64)))) -1/2)
(pow.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n))) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 2 n)))))
(/.f64 1 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 2 n))))
(/.f64 1 (pow.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))) -1/2))
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 n (/.f64 1 (PI.f64))))))
(sqrt.f64 (.f64 n (-.f64 (+.f64 1 (.f64 (/.f64 2 k) (PI.f64))) 1)))

Outputs
(sqrt.f64 (.f64 n (-.f64 (+.f64 1 (.f64 (/.f64 2 k) (PI.f64))) 1)))

Calls

3 calls:

11.0ms	(.f64 (.f64 2 (PI.f64)) n)
11.0ms	n
10.0ms	k

Results

Error	Segments	Branch
12.9b	1	`k`
12.9b	1	`n`
12.9b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 197 to 130 computations (34% saved)

regimes36.0ms (0%)

Counts

19 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)))
(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k))
(pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/2)
(pow.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64)))) -1/2)
(pow.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n))) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 2 n)))))
(/.f64 1 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 2 n))))
(/.f64 1 (pow.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))) -1/2))
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 n (/.f64 1 (PI.f64))))))

Outputs
(pow.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n))) -1/2)

Calls

3 calls:

11.0ms	(.f64 (.f64 2 (PI.f64)) n)
10.0ms	n
10.0ms	k

Results

Error	Segments	Branch
32.7b	1	`k`
32.7b	1	`n`
32.7b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 185 to 121 computations (34.6% saved)

regimes26.0ms (0%)

Counts

12 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)))
(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k))
(pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/2)
(pow.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64)))) -1/2)

Outputs
(pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/2)

Calls

3 calls:

8.0ms	k
7.0ms	n
7.0ms	(.f64 (.f64 2 (PI.f64)) n)

Results

Error	Segments	Branch
32.7b	1	`k`
32.7b	1	`n`
32.7b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 113 to 72 computations (36.3% saved)

regimes23.0ms (0%)

Counts

10 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)))
(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) k))

Outputs
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))

Calls

3 calls:

7.0ms	k
7.0ms	(.f64 (.f64 2 (PI.f64)) n)
6.0ms	n

Results

Error	Segments	Branch
32.7b	1	`k`
32.7b	1	`n`
32.7b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 95 to 61 computations (35.8% saved)

regimes13.0ms (0%)

Counts

8 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)))
(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))))

Outputs
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))))

Calls

2 calls:

6.0ms	k
5.0ms	n

Results

Error	Segments	Branch
32.8b	1	`k`
32.8b	1	`n`

Compiler

Compiled 72 to 46 computations (36.1% saved)

regimes13.0ms (0%)

Counts

7 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)))
(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))

Outputs
(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))

Calls

2 calls:

6.0ms	k
5.0ms	n

Results

Error	Segments	Branch
32.8b	1	`k`
32.8b	1	`n`

Compiler

Compiled 64 to 41 computations (35.9% saved)

regimes11.0ms (0%)

Accuracy

Total -0.4b remaining (-1.1%)

Threshold costs -0.4b (-1.1%)

Counts

5 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k 2))))
(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)))

Outputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))

Calls

2 calls:

5.0ms	k
4.0ms	n

Results

Error	Segments	Branch
32.8b	1	`k`
32.8b	1	`n`

Compiler

Compiled 48 to 31 computations (35.4% saved)

simplify15.0ms (0%)

Algorithm

1×	egg-herbie

Rules

19×	`*-commutative_binary64`
6×	`+-commutative_binary64`
5×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	87	366
1	114	366
2	122	366
3	126	366
4	128	366

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 n 2) (PI.f64))) (pow.f64 (.f64 (.f64 n 2) (PI.f64)) (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n 2) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k) (PI.f64))))))
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(if (<=.f64 k 2149935417987077/40564819207303340847894502572032) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(if (<=.f64 k 5399988732876221/20769187434139310514121985316880384) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 (.f64 n (-.f64 (+.f64 1 (.f64 (/.f64 2 k) (PI.f64))) 1))))
(if (<=.f64 k 8515366847997117/41538374868278621028243970633760768) (/.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (.f64 n (-.f64 (+.f64 1 (*.f64 (/.f64 2 k) (PI.f64))) 1))))
(if (<=.f64 k 376441522243775/1298074214633706907132624082305024) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 2 (/.f64 k (PI.f64))))) (sqrt.f64 (.f64 n (-.f64 (+.f64 1 (*.f64 (/.f64 2 k) (PI.f64))) 1))))
(sqrt.f64 (.f64 n (-.f64 (+.f64 1 (.f64 (/.f64 2 k) (PI.f64))) 1)))
(pow.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n))) -1/2)
(pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/2)
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))))
(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))

Outputs
(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 n 2) (PI.f64))) (pow.f64 (.f64 (.f64 n 2) (PI.f64)) (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n 2) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k) (PI.f64))))))
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 -1/2 (-.f64 1 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(if (<=.f64 k 2149935417987077/40564819207303340847894502572032) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(if (<=.f64 k 5399988732876221/20769187434139310514121985316880384) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 (.f64 n (-.f64 (+.f64 1 (.f64 (/.f64 2 k) (PI.f64))) 1))))
(if (<=.f64 k 5399988732876221/20769187434139310514121985316880384) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 (.f64 n (+.f64 (+.f64 1 (.f64 (PI.f64) (/.f64 2 k))) -1))))
(if (<=.f64 k 8515366847997117/41538374868278621028243970633760768) (/.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (.f64 n (-.f64 (+.f64 1 (*.f64 (/.f64 2 k) (PI.f64))) 1))))
(if (<=.f64 k 8515366847997117/41538374868278621028243970633760768) (/.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (.f64 n (+.f64 (+.f64 1 (*.f64 (PI.f64) (/.f64 2 k))) -1))))
(if (<=.f64 k 376441522243775/1298074214633706907132624082305024) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 2 (/.f64 k (PI.f64))))) (sqrt.f64 (.f64 n (-.f64 (+.f64 1 (*.f64 (/.f64 2 k) (PI.f64))) 1))))
(if (<=.f64 k 376441522243775/1298074214633706907132624082305024) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 2 (/.f64 k (PI.f64))))) (sqrt.f64 (.f64 n (+.f64 (+.f64 1 (*.f64 (PI.f64) (/.f64 2 k))) -1))))
(sqrt.f64 (.f64 n (-.f64 (+.f64 1 (.f64 (/.f64 2 k) (PI.f64))) 1)))
(sqrt.f64 (.f64 n (+.f64 (+.f64 1 (.f64 (PI.f64) (/.f64 2 k))) -1)))
(pow.f64 (/.f64 k (/.f64 (PI.f64) (/.f64 1/2 n))) -1/2)
(pow.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))) -1/2)
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (/.f64 1/2 n))))
(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) 2))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))

Compiler

Compiled 259 to 204 computations (21.2% saved)

soundness144.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

718×	`fma-def_binary64`
667×	`associate-/l*_binary64`
561×	`associate-/r*_binary64`
497×	`associate-/l*_binary64`
490×	`unswap-sqr_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	68	22
3	141	22
4	360	22
5	983	20
6	2213	20
7	5663	20
0	272	2833
1	619	2507
2	2252	2475

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 302 to 248 computations (17.9% saved)

end122.0ms (0.1%)

Compiler: Compiled 231 to 155 computations (32.9% saved)